Chapter 72, Problem 1A

Sketch a 251°25' ray on a Cartesian coordinate system and from a point on the ray sketch a right triangle. Label the sides of the triangle $+$ or $-$ . Determine the reference angle and the sine, cosine, tangent, cotangent, secant, and cosecant functions for the angle. Round the answers to 5 decimal places.

To determine

A ray of $251°25^{\prime }$, a right triangle from the ray, sine, cosine, tangent, cotangent, cosecant and secant.

Answer to Problem 1A

The sketch is shown in Figure 1 and all the trigonometry values are given below:

  $\sin 251°25^{\prime }=-0.94786$

  $\cos 251°25^{\prime }=-0.31868$

  $\tan 251°25^{\prime }=2.97430$

  $\cot 251°25^{\prime }=0.33621$

  $\text{cosec}251°25^{\prime }=-1.05501$

  $\text{sec}251°25^{\prime }=-3.13791$

Explanation of Solution

Given:

A ray of angle $220°10^{\prime }$.

Construction:

• Take a Cartesian plane and draw a ray of angle $251°25^{\prime }$ .
• Draw a right triangle from the point of the ray.
• Take negative sign on both base and height.

The sketch is shown below:

Figure 1.

Calculation:

All the trigonometry functions are calculated as follows:

  $\sin 251°25^{\prime }=-0.94786$

  $\cos 251°25^{\prime }=-0.31868$

  $\tan 251°25^{\prime }=2.97430$

  $\cot 251°25^{\prime }=0.33621$

  $\text{cosec}251°25^{\prime }=-1.05501$

  $\text{sec}251°25^{\prime }=-3.13791$

Conclusion:

The sketch is shown in Figure 1 and all the trigonometry values are given below:

  $\sin 251°25^{\prime }=-0.94786$

  $\cos 251°25^{\prime }=-0.31868$

  $\tan 251°25^{\prime }=2.97430$

  $\cot 251°25^{\prime }=0.33621$

  $\text{cosec}251°25^{\prime }=-1.05501$

  $\text{sec}251°25^{\prime }=-3.13791$