Trigonometry ( problems)

Question 1

how do we reduce expressions

Answer 1

Reduce expressions:

We simply the trig expression. Write the expression in terms of sine and cosine.

Question 2

how do we prove expressions

Answer 2

We do not need to solve the expression. We need to show that the LHS is equal to the RHS. Start with the more complex side.

Question 3

what is a reference angle

Answer 3

To solve trigonometric equations, we need to find areference angle, which is an angle that is always less than 90 degrees and lies in the first quadrant.

Question 4

why are trigonometric functions are periodic in nature

Answer 4

there can be multiple solutions to satisfy a given trigonometric equation

Question 5

how do we solve trigonometric equations

Answer 5

Step 1: Use mental calculations to find the reference angle.

Step 2: Use the CAST diagram to determine in which quadrants sinθ is positive.

Step 3: Write the final answer.

Step 1:Use a calculator to find the reference angle

Step 2:Use the CAST diagram to determine in which quadrantssinθis negative.

Step 3:Write the final answer.

Step 1: Use mental calculations to find the reference angle

Step 2: Use the CAST diagram to determine in which quadrants sinθ is negative.

Step 3: Write the final answer.

Step 1: Use a calculator to find the reference angle

Step 2: Use the CAST diagram to determine in which quadrants tanθ is negative.

Step 3: Write the final answer.