Given, sinθ=35 and 0≤θ≤π2

Answered: If sin e= and 0

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Analytic Trigonometry

Section2.3: Solving Trigonometric Equations

Problem 9ECP: Solve 4tan2x+5tanx6=0.

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Related questions

Question

If sin e=
and 0<es, find the exact value of tan 20.
%3D
4
24
24
4

Expert Solution

Step 1

$G i v e n, \sin (θ) = \frac{3}{5} a n d 0 \leq θ \leq \frac{π}{2}$

Step 2

$N o w, ∴ \sin (θ) = \frac{3}{5} S i n c e, θ l i e s i n t h e 2 n d q u a d r a n t, s o \cos (θ) w i l l b e p o s i t i v e . \Rightarrow \cos (θ) = \sqrt{1 - {(\sin (θ))}^{2}} \Rightarrow \cos (θ) = \sqrt{1 - {(\frac{3}{5})}^{2}} \Rightarrow \cos (θ) = \sqrt{1 - \frac{9}{25}} \Rightarrow \cos (θ) = \sqrt{\frac{16}{25}} \Rightarrow \cos (θ) = \frac{4}{5} ∴ \tan (θ) = \frac{\sin (θ)}{\cos (θ)} \Rightarrow \tan (θ) = \frac{\frac{3}{5}}{\frac{4}{5}} \Rightarrow \tan (θ) = \frac{3}{4}$