Question

Consider an angle with an initial ray pointing in the 3-o'clock direction that measures θ radians (where 0<θ<π2). The terminal point is hradius lengths to the right of the circle's center and v radius lengths above the circle's center. The slope of the angle's terminal ray is m. Match each of the following inputs/outputs with their corresponding variable. (You can use each variable once, more than once, or not at all.)

• -abcd The input of the cos−1 function
• -abcd The output of the cos−1 function
• -abcd The input of the sin−1 function
• -abcd The output of the sin−1 function
• -abcd The input of the tan−1 function
• -abcd The output of the tan−1 function

1. θ
2. h
3. m
4. v

Answer 1

The terminal point is h radius lengths to the right of the circle's center

So, cos $\theta$ = h

=> cos ^-1 (h) = $\theta$

The terminal point is v radius lengths above the circle's center

So, sin $\theta$ = v

=> sin ^-1 (v) = $\theta$

The slope of the angle's terminal ray is m

So, tan $\theta$ = m

=> tan ^-1 (m) = $\theta$

The input of the cos^-1 function is h

  The output of the cos^-1 function is $\theta$

  The input of the sin^-1 function is v

  The output of the sin^-1 function is $\theta$

The input of the tan^-1 function is m

  The output of the tan^-1 function is $\theta$