please help me solve a b c and d 8where sine < 0, find tan20.17If cose =Type the following information:a) QuadrantX =-y = r=b) Formulac) Substitute values into formulad) Answer

If cosθ=817 where sinθ<0, we have to find tan2θ cosθ=817cosθ=BCAC=817 let BC=8a and AC=17a…

Answered: 8 If cose where sine <0, find tan20. 17…

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter8: Complex Numbers And Polarcoordinates

Section8.3: Products And Quotients In Trigonometric Form

Problem 67PS

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please help me solve a b c and d

8
where sine < 0, find tan20.
17
If cose =
Type the following information:
a) Quadrant
X =
-y = r=
b) Formula
c) Substitute values into formula
d) Answer

Expert Solution

Step 1

If $\cos θ = \frac{8}{17}$ where sin $θ$ <0, we have to find tan2 $θ$

$\cos θ = \frac{8}{17} \cos θ = \frac{B C}{A C} = \frac{8}{17}$

let BC=8a and AC=17a

In $∆ A B C$ (right angle triangle) by Pythagoras's theorem.

AC²= BC² + AB²

(17a)² = (8a)² + AB²

289a²-64a²=AB²

AB² = 225a²

AB=15a

Step 2

$\sin θ = \frac{A B}{A C} \sin θ = \frac{15 a}{17 a} \sin θ = \frac{15}{17}$

but ; $\sin θ$ <0

$\Rightarrow \sin θ = \frac{- 15}{17}$

$\Rightarrow \tan θ = \frac{\sin θ}{\cos θ} = \frac{\frac{- 15}{17}}{\frac{8}{17}} \Rightarrow \tan θ = \frac{- 15}{8}$

FORMULA:-

$\tan 2 θ = \frac{2 \tan θ}{1 - {(\tan θ)}^{2}} s u b s t i t u t e v a l u e s i n t o f o r m u l a \tan 2 θ = \frac{\frac{2 (- 15)}{8}}{1 - {(\frac{- 15}{8})}^{2}} \tan 2 θ = \frac{\frac{- 30}{8}}{1 - \frac{225}{64}}$

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