Determine the exact value of the following trigonometric expression without the help of the calculator.

tan^-1 (tan 3π/4)

What is the value of cos^(-1)(-1)?

If sin(θ) = √2/2, what are all possible solutions for θ?

Is the given equation an identity?

$\cot^2x\cos^2x=\cot^2x+\sin^2x-1$

What is the exact value of sin(75°) using sum and difference identities?

Evaluate the expression cos(2θ) if θ = π/4 using double angle identities.

Which identity is used to express sin^2(θ) in terms of cos(θ)?

What is the Law of Sines?

Which formula represents the Law of Cosines for finding side c?

Which of the following formulas correctly represents the area of a triangle with sides b and c and angle A?

A vector makes a 45-degree angle with the east direction. What is the direction of the vector?

What is the component form of a vector with initial point (0, 0) and terminal point (5, 5)?

A vector has components (3, -4). In which quadrant is the vector located?

Is the vector 0.5i + 0.5j a unit vector?

Find a ⋅ b + a ⋅ c using the following vectors:

a = 9i - 4j, b = i + 5j, c = 8i + 3j

Calculate the cross product of vectors u = (1, 2, 3) and v = (4, 5, 6) using the matrix method.

What is the pole in the polar coordinate system?

What are the rectangular coordinates of the polar point (0, 0)?

What is the graph shape of the equation r = 6 cos(θ) after converting to rectangular form?

How many petals does the rose curve r = 3 sin 4θ have?

How do parametric equations differ from standard two-variable equations?

For the parametric equations x = 2cos(t) and y = 2sin(t), use a Pythagorean identity to eliminate the parameter and find the rectangular equation.

Why is it generally advised to avoid choosing t as an even power of x when parameterizing equations?

If you plot the complex number -2 + 5i, where will the point be located on the complex plane?

Which of the following is the correct polar form of the complex number -2 - 2i?