3. Find the exact values of the remaining five trig functions:sin 0 =239towhere sec 0 >0Using Reference Angles:ook Ingles not in the firsInstructions Use Referenceangle

We have given trigonometric equation sinθ=-23 Using formula sin2θ+cos2θ=1 cos2θ=1-sin2θ…

Answered: 3. Find the exact values of the…

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

See similar textbooks

Related questions

Question

3. Find the exact values of the remaining five trig functions:
sin 0 =
2
3
9
to
where sec 0 >0
Using Reference Angles:
ook In
gles not in the firs
Instructions Use Reference
angle

Expert Solution

Step 1

We have given trigonometric equation

$\sin θ = - \frac{2}{3}$

Using formula

$\sin^{2} θ + \cos^{2} θ$ $= 1$

$\cos^{2} θ = 1 -$ $\sin^{2} θ$

$\cos^{2} θ =$ $1 - {(- \frac{2}{3})}^{2} =$ $1 - \frac{4}{9} = \frac{5}{9}$

$\cos θ = |\frac{\sqrt{5}}{3}|$

$\cos θ >$ 0 as sec $θ > 0$

$\cos θ = \frac{\sqrt{5}}{3}$

sec $θ =$ $\frac{1}{\cos θ} =$ $\frac{3}{\sqrt{5}} = \frac{3 \sqrt{5}}{5}$

csc $θ = \frac{1}{\sin θ} = - \frac{3}{2}$

tan $θ = \frac{\sin θ}{\cos θ}$ $= - \frac{2}{\sqrt{5}} = - \frac{2 \sqrt{5}}{5}$

cot $θ = \frac{1}{\tan θ} =$ $- \frac{\sqrt{5}}{2}$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Recommended textbooks for you

Trigonometry (11th Edition)

Trigonometry

ISBN:

9780134217437

Author:

Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:

PEARSON

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781305652224

Author:

Charles P. McKeague, Mark D. Turner

Publisher:

Cengage Learning

Algebra and Trigonometry

Trigonometry

ISBN:

9781938168376

Author:

Jay Abramson

Publisher:

OpenStax

Trigonometry (11th Edition)

Trigonometry

ISBN:

9780134217437

Author:

Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:

PEARSON

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781305652224

Author:

Charles P. McKeague, Mark D. Turner

Publisher:

Cengage Learning

Algebra and Trigonometry

Trigonometry

ISBN:

9781938168376

Author:

Jay Abramson

Publisher:

OpenStax

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781337278461

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

3. Find the exact values of the remaining five trig functions: sin 0 2 3 9 where sec 0 >0 Instructions: