The answer is
a) 11/15
b) 1/18
Answer:
<h2>Definition of Reference Angle: Let θ be a non-quadrantal angle in </h2><h2>standard position. The reference angle of θ is the acute angle θR that the terminal side of θ makes with the x-axis. If θ is in QI, θR = θ If θ is in QII, θR = 180° – θ or π – θ</h2>
Step-by-step explanation:
<h2>
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![sinx=cosx-1 \\ \\ sinx-cosx=-1](https://tex.z-dn.net/?f=sinx%3Dcosx-1%20%5C%5C%20%20%5C%5C%20%0Asinx-cosx%3D-1)
Using the identity:
![sinx-cosx=- \sqrt{2}cos( \frac{ \pi }{4}+x)](https://tex.z-dn.net/?f=sinx-cosx%3D-%20%5Csqrt%7B2%7Dcos%28%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%2Bx%29%20%20)
, we get:
![- \sqrt{2}cos( \frac{ \pi }{4}+x)=-1 \\ \\ cos( \frac{ \pi }{4}+x)= \frac{1}{ \sqrt{2} } \\ \\ ](https://tex.z-dn.net/?f=-%20%5Csqrt%7B2%7Dcos%28%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%2Bx%29%3D-1%20%5C%5C%20%20%5C%5C%20%0Acos%28%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%2Bx%29%3D%20%5Cfrac%7B1%7D%7B%20%5Csqrt%7B2%7D%20%7D%20%5C%5C%20%20%5C%5C%20%0A%20)
There are two solutions to this equation:
1) ![\frac{ \pi }{4}+x= \frac{ \pi }{4} \\ \\ x=0](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%2Bx%3D%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20%0Ax%3D0%20%20)
Since the period of cosine is 2π, so 0 + 2π = 2π will also be a solution to the given equation
2)
Therefore, there are 3 solutions to the given trigonometric equation.
<h3>
Answer:</h3>
36 ft
<h3>
Step-by-step explanation:</h3>
The area of a rectangle is the product of length and width. Here, you have the width being 2/3 the length. Put the given values into the area formula and solve.
A = L·W
864 ft² = L · (2/3·L)
1296 ft² = L² . . . . . . . multiply by 3/2
36 ft = L . . . . . . . . . . . take the square root
The length of Louis's basement is 36 feet.
Total room in the 2 suitcases is 33 ft³
Step-by-step explanation:
- Step 1: To find the total room in the suitcases, find volume of the suitcases, given by V = length × width × height
⇒ Volume of 1st suitcase = 3 × 2 × 4 = 24 ft³
⇒ Volume of 2nd suitcase = 3 × 1 × 3 = 9 ft³
∴ Total room in Sandra's suitcases = 24 + 9 = 33 ft³