Can you help me with this? 1. If sin 0= 1, find the exact value of the following, with <0 < T.а.Cos eb. sin(20)с.tan

Name: Can you help me with this? 1. If sin 0= 1, find the exact value of the
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Description: Can you help me with this? 1. If sin 0= 1, find the exact value of the following, with <0 < T.а.Cos eb. sin(20)с.tan

Given: sin θ = 45, π2≤θ≤π

Answered: 1. If sin 0 =, find the exact value of…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Analytic Trigonometry

Section2.4: Sum And Difference Formulas

Problem 3ECP: Find the exact value of cosu+v given sinu=1213, where 0u2 and cosv=35, where 2v.

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Can you help me with this?

1. If sin 0
= 1, find the exact value of the following, with <0 < T.
а.
Cos e
b. sin(20)
с.
tan

Expert Solution

Step 1

Given:

$\sin θ = \frac{4}{5}, \frac{π}{2} \leq θ \leq π$

Step 2

Formulae to be used:

For any angle, $θ$

$1 . \sin^{2} (θ) + \cos^{2} (θ) = 1 2 . \sin (2 θ) = 2 \sin (θ) \cos (θ) 3 . \tan (\frac{θ}{2}) = \frac{\sin (θ)}{1 + \cos (θ)}$

Step 3

Since, $\sin^{2} (θ) + \cos^{2} (θ) = 1$

Therefore,

$\cos (θ) = \pm \sqrt{1 - \sin^{2} (θ)}$

Plug $\sin (θ) = \frac{4}{5}$ , to get

$\begin{array}{rcl} \cos (θ) & = & \pm \sqrt{1 - {(\frac{4}{5})}^{2}} \\ = & \pm \sqrt{1 - \frac{16}{25}} \\ = & \pm \sqrt{\frac{25 - 16}{25}} \\ = & \pm \sqrt{\frac{9}{25}} \\ = & \pm \frac{3}{5} \end{array}$

But $θ$ lies in second quadrant and cosine function gives negative values in second quadrant.

Hence,

$c o s (θ) = - \frac{3}{5}$

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