Find Trig Functions Using Identities tan(theta)=-3/5 , cos(theta)>0

Find Trig Functions Using Identities tan(theta)=-3/5 , cos(theta)>0
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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 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.
Simplify inside the radical.
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Raise to the power of .
Hypotenuse
Raise to the power of .
Hypotenuse
Add and .
Hypotenuse
Hypotenuse
Find the value of sine.
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Use the definition of sine to find the value of .
Substitute in the known values.
Simplify the value of .
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Move the negative in front of the fraction.
Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Find the value of cosine.
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Use the definition of cosine to find the value of .
Substitute in the known values.
Simplify the value of .
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Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Find the value of cotangent.
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Use the definition of cotangent to find the value of .
Substitute in the known values.
Move the negative in front of the fraction.
Find the value of secant.
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Use the definition of secant to find the value of .
Substitute in the known values.
Find the value of cosecant.
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Use the definition of cosecant to find the value of .
Substitute in the known values.
Move the negative in front of the fraction.
This is the solution to each trig value.
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Name

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

Interesting facts

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

Basic properties

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

Name

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

Interesting facts

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

Basic properties

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

Name

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

Interesting facts

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

Basic properties

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