Answer:
The sine and cosine functions have a period of 2π radians and the tangent function has a period of π radians. Domain and range: From the graphs above we see that for both the sine and cosine functions the domain is all real numbers and the range is all reals from −1 to +1 inclusive.
Step-by-step explanation:
Answer:
5. Plane P
6. Line segment DB
7. Line CE
11. Ray BE (with an arrow on top from left to right) and Ray EC (with an arrow on top from left to right)
Step-by-step explanation:
Left hand side:
4 [sin⁶ θ + cos⁶ θ]
Rearrange:
4 [(sin² θ)³ + (cos² θ)³]
Factor the sum of cubes:
4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]
Pythagorean identity:
4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]
Complete the square:
4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]
4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]
Pythagorean identity:
4 [1 − 3 sin² θ cos² θ]
Rearrange:
4 − 12 sin² θ cos² θ
4 − 3 (2 sin θ cos θ)²
Double angle formula:
4 − 3 (sin (2θ))²
4 − 3 sin² (2θ)
Finally, apply Pythagorean identity and simplify:
4 − 3 (1 − cos² (2θ))
4 − 3 + 3 cos² (2θ)
1 + 3 cos² (2θ)
Change 13% as a fraction. It will be 13/100
Now, which is bigger? 13/100 or 3/25
Cross multiply and 13/100 is bigger.
13 3
___ X ____
100 25
13×25=325 and 3×100=300. Now you know 13/100 is bigger.
The answer is 13/100
