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:

Find the following trigonometric values. Express your answers exactly. {:[cos(225^(@))=],[sin(225^(@))=]:}

Find the following trigonometric values.\newlineExpress your answers exactly.\newlinecos⁡(225∘)=sin⁡(225∘)= \begin{array}{l} \cos \left(225^{\circ}\right)= \\ \sin \left(225^{\circ}\right)= \end{array}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Evaluate exponential functionsright chevron icon

Full solution

Q. Find the following trigonometric values.\newlineExpress your answers exactly.\newlinecos⁡(225∘)=sin⁡(225∘)= \begin{array}{l} \cos \left(225^{\circ}\right)= \\ \sin \left(225^{\circ}\right)= \end{array}
  1. Recognizing the third quadrant: To find the exact values of cos⁡(225∘)\cos(225^\circ) and sin⁡(225∘)\sin(225^\circ), we need to recognize that 225∘225^\circ is in the third quadrant where both cosine and sine are negative. We can also use the reference angle of 45∘45^\circ because 225∘225^\circ is 180∘+45∘180^\circ + 45^\circ.
  2. Using the reference angle: The cosine and sine of 45∘45^\circ are known exact values. Since 225∘225^\circ is in the third quadrant, we will use the negative of these values.\newlinecos⁡(45∘)=sin⁡(45∘)=22\cos(45^\circ) = \sin(45^\circ) = \frac{\sqrt{2}}{2}\newlineTherefore, cos⁡(225∘)=−cos⁡(45∘)\cos(225^\circ) = -\cos(45^\circ) and sin⁡(225∘)=−sin⁡(45∘)\sin(225^\circ) = -\sin(45^\circ).
  3. Calculating the exact values: Now we calculate the exact values using the reference angle:\newlinecos(225225∘ ^\circ ) = -cos(4545∘ ^\circ ) = -22 \frac{\sqrt{2}}{2} \newlinesin(225225∘ ^\circ ) = -sin(4545∘ ^\circ ) = -22 \frac{\sqrt{2}}{2}

More problems from Evaluate exponential functions

Question
A 13 km 13 \mathrm{~km} stretch of road needs repairs. Workers can repair 312 km 3 \frac{1}{2} \mathrm{~km} of road per week.\newlineHow many weeks will it take to repair this stretch of road?\newlineweeks
Get tutor helpright-arrow

Posted 10 months ago

Question
Liam opened a savings account and deposited $6000 \$ 6000 . The account earns 5% 5 \% in interest annually. He makes no further deposits and does not withdraw any money. In t t years, he has $8865 \$ 8865 in this account.\newlineWrite an equation in terms of t t that models the situation.
Get tutor helpright-arrow

Posted 10 months ago

Question
Samantha opened a savings account and deposited $8192 \$ 8192 . The account earns 10% 10 \% in interest annually. She makes no further deposits and does not withdraw any money. In t t years, she has $25,710 \$ 25,710 in this account.\newlineWrite an equation in terms of t t that models the situation.
Get tutor helpright-arrow

Posted 10 months ago

Question
The graph of a sinusoidal function intersects its midline at (0,−7) (0,-7) and then has a minimum point at (π4,−9) \left(\frac{\pi}{4},-9\right) .\newlineWrite the formula of the function, where x x is entered in radians.\newlinef(x)= f(x)=
Get tutor helpright-arrow

Posted 10 months ago

Question
The following formula is used in economics to find a company's gross profit rate P P , where S S is the net sales and C C is the cost of goods sold.\newlineP=S−CS P=\frac{S-C}{S} \newlineRearrange the formula to highlight the cost of goods sold.\newlineC=□ C=\square
Get tutor helpright-arrow

Posted 10 months ago

Question
3⋅50.2w=720 3 \cdot 5^{0.2 w}=720 \newlineWhat is the solution of the equation?\newlineRound your answer, if necessary, to the nearest thousandth.\newlinew≈ w \approx
Get tutor helpright-arrow

Posted 10 months ago

Question
18⋅25t=261 18 \cdot 2^{5 t}=261 \newlineWhat is the solution of the equation?\newlineRound your answer, if necessary, to the nearest thousandth.\newlinet≈ t \approx
Get tutor helpright-arrow

Posted 10 months ago

Question
−4⋅36w=−1750 -4 \cdot 3^{6 w}=-1750 \newlineWhat is the solution of the equation?\newlineRound your answer, if necessary, to the nearest thousandth.\newlinew≈ w \approx
Get tutor helpright-arrow

Posted 10 months ago

Question
20⋅73y=5 20 \cdot 7^{3 y}=5 \newlineWhat is the solution of the equation?\newlineRound your answer, if necessary, to the nearest thousandth.\newliney≈ y \approx
Get tutor helpright-arrow

Posted 10 months ago

Question
10⋅35t4=800 10 \cdot 3^{\frac{5 t}{4}}=800 \newlineWhat is the solution of the equation?\newlineRound your answer, if necessary, to the nearest thousandth.\newlinet≈ t \approx
Get tutor helpright-arrow

Posted 10 months ago

View all (45)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant