Chapter 7: Q. 39 (page 495)

$f (x) = \sin x, g (x) = \cos x$ use the figures to evaluate each function given that and $h (x) = \tan x$ .
$h (\frac{α}{2})$

Short Answer

Expert verified

Thus

$h (\frac{α}{2}) = \tan (\frac{α}{2}) = - \frac{\sqrt{15}}{3}$

Step by step solution

Step 1. Given

$h (x) = \tan x t h u s h (\frac{α}{2}) = \tan (\frac{α}{2})$

Step 2. Concept

we will use standard trigonometric formula's for solving the given expression.

Using half-angle formula

$\tan (\frac{α}{2}) = \frac{\sin α}{1 + \cos α}$

Step 3. Calculation

We have

$\cos α = - \frac{1}{4}, \sin α = b a s t h e p o i n t (- \frac{1}{4}, b) l i e s o n t h e c i r c l e x^{2} + y^{2} = 1 N o w {(- \frac{1}{4})}^{2} + b^{2} = 1 b^{2} = 1 - \frac{1}{16} b^{2} = \frac{15}{16} b = \pm \frac{\sqrt{15}}{4} S i n c e p o i n t l i e i n t h e 3^{r d} q u a d r a n t t h e r e f o r e b w i l l b e n e g a t i v e t h u s, \sin α = - \frac{\sqrt{15}}{4} S u b s t i t u t i n g t h e v a l u e o f \sin α & \cos α i n h a l f - a n g l e f o r m u l a w e g e t \tan (\frac{α}{2}) = \frac{- \frac{\sqrt{15}}{4}}{1 + (- \frac{1}{4})} = - \frac{\sqrt{15}}{3}$

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$f (x) = \sin x, g (x) = \cos x$ use the figures to evaluate each function given that and $h (x) = \tan x$ .
$h (\frac{α}{2})$

Short Answer

Step by step solution

Step 1. Given

Step 2. Concept

Step 3. Calculation

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f(x)=sinx,g(x)=cosxuse the figures to evaluate each function given that and h(x)=tanx.hα2

Short Answer

Step by step solution

Step 1. Given

Step 2. Concept

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Study anywhere. Anytime. Across all devices.

$f (x) = \sin x, g (x) = \cos x$ use the figures to evaluate each function given that and $h (x) = \tan x$ .
$h (\frac{α}{2})$