Question

This is my first calculus class and I am lost on how to answer these. The book isn't giving me a clear explanation for help. Any help someone could provide would be great!

1. Use a reference triangle to find the given angle.
cos -1 (1/2) give an exact answer in terms of pi

2. Express In 0.25 in terms of In 2 and In 3. Simplify your answer. Use integers or fractions for any number in the answer.

3. Determine whether the function is even, odd or neither.
f(x)=4x^5 + 3x^3

Thank you!!!!

Answer 1

1. Use a reference triangle to find the given angle.
cos -1 (1/2) give an exact answer in terms of pi

adjacent/hypotenuse = 1/2
well, if you know about 30,60,90 triangle the answer is immediate.
sin 30 degrees = 1/2
cos 60 degrees = 1/2
60 degrees = pi/3 radians

Answer 2

2. Express In 0.25 in terms of In 2 and In 3. Simplify your answer. Use integers or fractions for any number in the answer.

ln (1/4) = ln 1 - ln 4 = 0 - ln 4

-ln 4 = -2 ln 2

Answer 3

3. Determine whether the function is even, odd or neither.
f(x)=4x^5 + 3x^3

For negative x, this function is negative of the corresponding value for positive x
Therefore it is ODD
In general odd powers of x are odd and even powers of x are even
eg
f(x ) = +x
f(-x) = -x odd

f(x ) = + x^2
f(-x) = + x^2 even