Question
If $\theta$ is an acute angle, find the other trigonometric functions of $\theta$, given(a) $\sin \theta=\frac{12}{13}$; (b) $\cos \theta=\frac{5}{7}$; (c) $\tan \theta=\frac{1}{\sqrt{2}}$.
Step 1
Since \(\theta\) is an acute angle, we can use the Pythagorean identity \(\sin^2 \theta + \cos^2 \theta = 1\) to find \(\cos \theta\). Show more…
Show all steps
Your feedback will help us improve your experience
Urvashi Arora and 53 other educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Angle $\theta$ is in quadrant II and $\sin \theta=\frac{5}{13} .$ Determine an exact value for each of the following. a) $\cos 2 \theta$ b) $\sin 2 \theta$ c) $\sin \left(\theta+\frac{\pi}{2}\right)$
Trigonometric Identities
Sum, Difference, and Double-Angle Identities
If $\theta=\cos ^{-1}(4 / 5)+\tan ^{-1}(2 / 3)$ then (a) $\sin \theta=\frac{17}{5 \sqrt{13}}$ (b) $\cos \theta=\frac{6}{5 \sqrt{13}}$ (c) $\tan \theta=17 / 6$ (d) $\cot \theta=17 / 6$
$\theta$ is an acute angle and sin u and cos u are given. Use identities to find tan $\theta$, csc $\theta$, sec $\theta$, and cot $\theta$. Where necessary, rationalize denominators. $$ \sin \theta=\frac{6}{7}, \quad \cos \theta=\frac{\sqrt{13}}{7} $$
Trigonometric Functions
Right Triangle Trigonometry
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD