# Find the angles

• Nov 10th 2007, 06:48 AM
finalfantasy
Find the angles
Find the angle Θ, 0 Θ ≤ 2 pi

Cos Θ = 0.2157 Tan Θ =-0.7147

The answers I were given show 2 answers can be found. Can someone tell me the answers for both questions and explain how it can be found.

THANK YOU.
• Nov 10th 2007, 08:07 AM
Soroban
Hello, finalfantasy!

Quote:

Find the angle $\displaystyle \theta,\;\;0 \leq \theta \leq 2\pi$

. . $\displaystyle \cos\theta = 0.2157,\;\;\tan\theta = -0.7147$

Only one angle is possible.

Cosine is positive in Quadrants 1 and 4.
Tangent is negative in Quadrants 2 and 4.
. . Hence, $\displaystyle \theta$ is in Quadrant 4 . . . so where's the other angle?

• Nov 10th 2007, 08:17 AM
finalfantasy
Those are 2 separate questions ^^;

1. Cos Θ = 0.2157

2. Tan Θ =-0.7147
• Nov 10th 2007, 12:54 PM
Soroban
Hello, finalfantasy!

Don't you have inverse trig functions on your calculator?

Quote:

$\displaystyle 1.\;\;\cos\theta \:=\:0.2157$

$\displaystyle \theta \:=\:\cos^{-1}(0.2157) \;\approx\;1.35,\;4.93$ radians

Quote:

$\displaystyle 2.\;\;\tan\theta \:=\:0.7147$

$\displaystyle \theta \:=\:\tan^{-1}(0.7147) \:\approx\:0.62,\;3.76$ radians

• Nov 10th 2007, 07:31 PM
finalfantasy
Hmm ... those were the answers on my sheet, I got the first answer for each of those questions, but how do you get the second? o-o;
• Nov 11th 2007, 03:37 AM
Macleef
Quote:

Originally Posted by finalfantasy
Find the angle Θ, 0 Θ ≤ 2 pi

Cos Θ = 0.2157 Tan Θ =-0.7147

The answers I were given show 2 answers can be found. Can someone tell me the answers for both questions and explain how it can be found.

THANK YOU.

Use the inverse function in your calculator,

1. Cos^{-1}(0.2157) = 78
2. Tan^{-1}(-0.7147) = -36

I think you want the answer in both approximate and exact form, right? Or, find the two angles?

To find the radians, you must convert degrees to radians, to do so:
(degree) x (pi / degree)
If you want to find the degrees from radians:

1. Cos^{-1}(0.2157) = 78

78 x pi/180
= 78pi/180

To find the other angle in quadrant 4, you do your principle angle:
360 -
Θ
= 360 - 78
= 282

282 x pi/180
= 282pi/180

2. Tan^{-1}(-0.7147) = -36

Since the degree is a negative, the angle will be in the second and fourth quadrant because in the first and third quadrant, the angle would be in positive, hence, CAST rule

First, you must find your related angle, which is 36 in this case

36 x pi/180
= 36pi/180