# Find the Other Trig Values in Quadrant III cos(theta)=-( square root of 8)/3

Find the Other Trig Values in Quadrant III cos(theta)=-( square root of 8)/3
Use the definition of cosine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Find the opposite side of the unit circle triangle. Since the adjacent side and hypotenuse are known, use the Pythagorean theorem to find the remaining side.
Replace the known values in the equation.
Negate .
Opposite
Raise to the power of .
Opposite
Rewrite as .
Factor out of .
Opposite
Rewrite as .
Opposite
Opposite
Pull terms out from under the radical.
Opposite
Multiply by .
Opposite
Apply the product rule to .
Opposite
Raise to the power of .
Opposite
Rewrite as .
Use to rewrite as .
Opposite
Apply the power rule and multiply exponents, .
Opposite
Combine and .
Opposite
Cancel the common factor of .
Cancel the common factor.
Opposite
Rewrite the expression.
Opposite
Opposite
Evaluate the exponent.
Opposite
Opposite
Multiply by .
Opposite
Multiply by .
Opposite
Subtract from .
Opposite
Any root of is .
Opposite
Multiply by .
Opposite
Opposite
Find the value of sine.
Use the definition of sine to find the value of .
Substitute in the known values.
Move the negative in front of the fraction.
Simplify the numerator.
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Find the value of tangent.
Use the definition of tangent to find the value of .
Substitute in the known values.
Simplify the value of .
Dividing two negative values results in a positive value.
Simplify the denominator.
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Combine and simplify the denominator.
Multiply and .
Move .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Multiply by .
Find the value of cotangent.
Use the definition of cotangent to find the value of .
Substitute in the known values.
Simplify the value of .
Dividing two negative values results in a positive value.
Divide by .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Find the value of secant.
Use the definition of secant to find the value of .
Substitute in the known values.
Simplify the value of .
Simplify the denominator.
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Move the negative in front of the fraction.
Multiply by .
Combine and simplify the denominator.
Multiply and .
Move .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Multiply by .
Find the value of cosecant.
Use the definition of cosecant to find the value of .
Substitute in the known values.
Divide by .
This is the solution to each trig value.
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### Name

Name nine hundred fourteen million one hundred forty thousand three hundred ninety-two

### Interesting facts

• 914140392 has 64 divisors, whose sum is 3189352320
• The reverse of 914140392 is 293041419
• Previous prime number is 307

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 33
• Digital Root 6

### Name

Name one hundred ninety-three million three hundred thirty-eight thousand six hundred thirty-four

### Interesting facts

• 193338634 has 8 divisors, whose sum is 294923520
• The reverse of 193338634 is 436833391
• Previous prime number is 59

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 40
• Digital Root 4

### Name

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

### Interesting facts

• 1220271875 has 4 divisors, whose sum is 1220665488
• The reverse of 1220271875 is 5781720221
• Previous prime number is 3125

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 35
• Digital Root 8