Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Express as a function of a DIFFERENT angle, 0^(@) <= theta < 360^(@). tan(324^(@)) tan(◻^(@))

Express as a function of a DIFFERENT angle, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlinetan⁡(324∘) \tan \left(324^{\circ}\right) \newlinetan⁡(□∘) \tan \left(\square^{\circ}\right)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Find trigonometric ratios using reference anglesright chevron icon

Full solution

Q. Express as a function of a DIFFERENT angle, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlinetan⁡(324∘) \tan \left(324^{\circ}\right) \newlinetan⁡(□∘) \tan \left(\square^{\circ}\right)
  1. Understand the problem: Understand the problem.\newlineWe need to express tan⁡(324°)\tan(324°) as a function of a different angle within the range of 0°0° to 360°360°. To do this, we can use the periodic properties of the tangent function and the fact that it is negative in the fourth quadrant, where 324°324° lies.
  2. Find reference angle: Find the reference angle for 324°324°. The reference angle is the acute angle that the terminal side of the angle makes with the x-axis. For an angle in the fourth quadrant, the reference angle is 360°−θ360° - \theta. So, the reference angle for 324°324° is 360°−324°=36°360° - 324° = 36°.
  3. Use reference angle: Use the reference angle to express tan⁡(324°)\tan(324°). Since tan⁡(θ)=tan⁡(θ+n⋅180°)\tan(\theta) = \tan(\theta + n\cdot180°) for any integer nn, and the tangent function is negative in the fourth quadrant, we can express tan⁡(324°)\tan(324°) as −tan⁡(36°)-\tan(36°).

More problems from Find trigonometric ratios using reference angles

Question
Find all solutions with 0∘≤θ≤180∘0^\circ \leq \theta \leq 180^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinecos⁡(θ)=−1\cos(\theta) = -1\newline‾∘\underline{\hspace{2em}}^\circ
Get tutor helpright-arrow

Posted 1 month ago

Question
Kimi's school is 1515 kilometers west of her house and 88 kilometers south of her friend Franklin's house. Every day, Kimi bicycles from her house to her school. After school, she bicycles from her school to Franklin's house. Before dinner, she bicycles home on a bike path that goes straight from Franklin's house to her own house. How far does Kimi bicycle each day?\newline_____\_\_\_\_\_ kilometers
Get tutor helpright-arrow

Posted 1 month ago

Question
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.\newlinecos⁡35∘=\cos 35^\circ = __
Get tutor helpright-arrow

Posted 1 month ago

Question
Find all solutions with −90∘≤θ≤90∘-90^\circ \leq \theta \leq 90^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinecsc⁡(θ)=−1\csc(\theta) = -1\newline____ ∘\_\_\_\_\,^\circ
Get tutor helpright-arrow

Posted 1 month ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecot⁡30∘=\cot 30^\circ = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
The terminal side of an angle θ\theta in standard position intersects the unit circle at (8485,1385)(\frac{84}{85}, \frac{13}{85}). What is cos⁡(θ)\cos(\theta)?\newlineWrite your answer in simplified, rationalized form.\newline______
Get tutor helpright-arrow

Posted 1 month ago

Question
−90∘<θ<90∘-90^\circ < \theta < 90^\circ. Find the value of θ\theta in degrees.\newlinetan⁡(θ)=0\tan(\theta) = 0\newlineWrite your answer in simplified, rationalized form. Do not round.\newlineθ=\theta = ____∘^\circ\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecsc⁡60∘=\csc 60^\circ = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
θ\theta is an acute angle. Find the value of θ\theta in degrees.\newlinesec⁡(θ)=2\sec(\theta) = \sqrt{2}\newlineθ=\theta = ____°\degree
Get tutor helpright-arrow

Posted 1 month ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecos⁡90∘=\cos 90^\circ = ____
Get tutor helpright-arrow

Posted 2 months ago

View all (102)