# What is the period of #f(theta) = tan ( ( 3 theta)/4 )- cos ( ( theta)/ 5 ) #?

(4pi/3) x 15 --> 20pi 10pi x 2 --> 20pi

By signing up, you agree to our Terms of Service and Privacy Policy

To find the period of the function ( f(\theta) = \tan\left(\frac{3\theta}{4}\right) - \cos\left(\frac{\theta}{5}\right) ), we need to identify the smallest positive value of ( p ) such that ( f(\theta + p) = f(\theta) ) for all ( \theta ).

The period of ( \tan(ax) ) is ( \frac{\pi}{|a|} ), and the period of ( \cos(bx) ) is ( \frac{2\pi}{|b|} ).

For ( \tan\left(\frac{3\theta}{4}\right) ), the period is ( \frac{4\pi}{3} ).

For ( \cos\left(\frac{\theta}{5}\right) ), the period is ( 10\pi ).

The least common multiple (LCM) of ( \frac{4\pi}{3} ) and ( 10\pi ) is ( 20\pi ).

Therefore, the period of ( f(\theta) ) is ( 20\pi ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you graph #y=cos(x-pi)#?
- How do you find an angle between 0 and 2 pi that is coterminal with -19/24 pi express answer in radians?
- How do you convert #(13pi)/9# into degrees?
- How do you graph #y=6csc(3x+(2pi)/3)-2#?
- How do you use transformation to graph the sin function and determine the amplitude and period of #y=sin(x+pi/6)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7