Show all steps 4.元Suppose that sin 0 = and2.Find the exact values of cosand tan22Cos2.tan2.

As we know sin2θ+cos2θ=1. cosθ=1-452=1-1625=-35 Using Double angle formula: sinθ2=1-cosθ2=1+352=810…

Answered: 4 Suppose that sin e -and <0<1. Find…

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Trigonometry

4 Suppose that sin e -and <0<1. Find the exact values of cos 2 and tan 2. Cos 2. = D tan, 2) %3D

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section: Chapter Questions

Problem 73RE

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Question

Show all steps

4.
元
Suppose that sin 0 = and
2.
Find the exact values of cos
and tan
2
2
Cos
2.
tan
2.

Expert Solution

Step 1

As we know $\sin^{2} θ + \cos^{2} θ = 1$ .

$\begin{array}{rcl} \cos θ & = & \sqrt{1 - {(\frac{4}{5})}^{2}} \\ = & \sqrt{1 - \frac{16}{25}} \\ = & - \frac{3}{5} \end{array}$

Using Double angle formula:

$\begin{array}{rcl} \sin \frac{θ}{2} & = & \sqrt{\frac{1 - \cos θ}{2}} \\ = & \sqrt{\frac{1 + \frac{3}{5}}{2}} \\ = & \sqrt{\frac{8}{10}} \end{array}$

$\begin{array}{rcl} \cos \frac{θ}{2} & = & \sqrt{\frac{1 - 3 / 5}{2}} \\ = & \sqrt{\frac{2}{10}} \end{array}$

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