The cosine function is positive in the first and fourth quadrants. The tangent function is negative in the second and fourth quadrants. The set of solutions for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> are limited to the fourth quadrant since that is the only quadrant found in both sets.

Solution is in the fourth quadrant.

Use the definition of tangent to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

Find the hypotenuse of the unit circle triangle. Since the opposite and adjacent sides are known, use the Pythagorean theorem to find the remaining side.

Replace the known values in the equation.

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Hypotenuse <math><mstyle displaystyle="true"><mo>=</mo><msqrt><mn>9</mn><mo>+</mo><msup><mrow><mo>(</mo><mn>5</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mstyle></math>

Raise <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Hypotenuse <math><mstyle displaystyle="true"><mo>=</mo><msqrt><mn>9</mn><mo>+</mo><mn>25</mn></msqrt></mstyle></math>

Add <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Hypotenuse <math><mstyle displaystyle="true"><mo>=</mo><msqrt><mn>34</mn></msqrt></mstyle></math>

Hypotenuse <math><mstyle displaystyle="true"><mo>=</mo><msqrt><mn>34</mn></msqrt></mstyle></math>

Use the definition of sine to find the value of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Substitute in the known values.

Simplify the value of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Move the negative in front of the fraction.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><msqrt><mn>34</mn></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>34</mn></msqrt></mrow><mrow><msqrt><mn>34</mn></msqrt></mrow></mfrac></mstyle></math> .

Combine and simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><msqrt><mn>34</mn></msqrt></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>34</mn></msqrt></mrow><mrow><msqrt><mn>34</mn></msqrt></mrow></mfrac></mstyle></math> .

Raise <math><mstyle displaystyle="true"><msqrt><mn>34</mn></msqrt></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><msqrt><mn>34</mn></msqrt></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><msqrt><mn>34</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>34</mn></mstyle></math> .

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mn>34</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>34</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate the exponent.

Use the definition of cosine to find the value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Substitute in the known values.

Simplify the value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><msqrt><mn>34</mn></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>34</mn></msqrt></mrow><mrow><msqrt><mn>34</mn></msqrt></mrow></mfrac></mstyle></math> .

Combine and simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><msqrt><mn>34</mn></msqrt></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>34</mn></msqrt></mrow><mrow><msqrt><mn>34</mn></msqrt></mrow></mfrac></mstyle></math> .

Raise <math><mstyle displaystyle="true"><msqrt><mn>34</mn></msqrt></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><msqrt><mn>34</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>34</mn></mstyle></math> .

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mn>34</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>34</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate the exponent.

Use the definition of cotangent to find the value of <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Substitute in the known values.

Move the negative in front of the fraction.

Use the definition of secant to find the value of <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Substitute in the known values.

Use the definition of cosecant to find the value of <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Substitute in the known values.

Move the negative in front of the fraction.

This is the solution to each trig value.

Do you know how to Find Trig Functions Using Identities tan(theta)=-3/5 , cos(theta)>0? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | one billion four hundred thirty-seven million one hundred eleven thousand six hundred ninety-six |
---|

- 1437111696 has 128 divisors, whose sum is
**9764794944** - The reverse of 1437111696 is
**6961117341** - Previous prime number is
**151**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 39
- Digital Root 3

Name | one billion nine hundred eighty-three million eight thousand eight hundred seventy-eight |
---|

- 1983008878 has 16 divisors, whose sum is
**3003858000** - The reverse of 1983008878 is
**8788003891** - Previous prime number is
**2339**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 52
- Digital Root 7

Name | one billion sixty-two million five hundred seventy-seven thousand eight hundred twenty-seven |
---|

- 1062577827 has 16 divisors, whose sum is
**1889377920** - The reverse of 1062577827 is
**7287752601** - Previous prime number is
**9539**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 45
- Digital Root 9