Chapter 6: Q. 90 (page 381)

If $f (x) = \cos θ = 0.3,$ findrole="math" localid="1647539382705" $f (θ + π)$

Short Answer

Expert verified

The value of $f (θ + π) = - 0.3$

Step by step solution

Step 1. Given information

$f (θ) = \cos θ = 0.3$

Step 2. Finding the value of f(θ+π)

For an angle $θ$ is standard position,let $P = (x, y)$ be the point on the terminal side of $θ$ that is also on the circle localid="1647539950698" $x^{2} + y^{2} = r^{2}$ .Then

localid="1647539956108" $\sin θ = \frac{y}{r} \cos θ = \frac{x}{r} \tan θ = \frac{y}{x} c s c θ = \frac{r}{y} s e c θ = \frac{r}{x} c o t θ = \frac{x}{y}$

Consider $f (θ) = = \cos θ = 0.3$

That is $\cos θ = \frac{x}{r} = 0.3$

sothat x is positive

therefore, $θ$ is in 1st quadrants

Then $θ + π$ is in the 2nd and 3rd quadrant so that xis negtive

Hence,

localid="1647539987909" $f (θ + π) = \frac{- x}{r} = - \cos θ = - 0.3$

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If $f (x) = \cos θ = 0.3,$ findrole="math" localid="1647539382705" $f (θ + π)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the value of f(θ+π)

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Iff(x)=cosθ=0.3,findrole="math" localid="1647539382705" f(θ+π)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the value of f(θ+π)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Probability and Statistics

Applied Mathematics

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

If $f (x) = \cos θ = 0.3,$ findrole="math" localid="1647539382705" $f (θ + π)$