#10 Trig Identities and Equations

What is a unit circle?

A circle with a radius of 1 unit

On a unit circle, where are positive angle measured from and how?

Anticlockwise from the positive x-axis

Describe how a CAST diagram works.

CAST diagrams show which identity is positive in each section

→ in the C section, CosX is positive

→ in the A section, all are positive

→ in the S section, SinX is positive

→ in the T section, TanX is positive

State the exact value for Sin30.

½

State the exact value for Cos30.

root 3 / 2

State the exact value for Tan30.

root 3/ 3

State the exact value for Sin60.

root 3 / 2

State the exact value for Cos60.

½

State the exact value for Tan60.

root 3

State the exact value for Sin45.

root 2 / 2

State the exact value for Cos45.

root 2 / 2

State the exact value for Tan45.

1

State both trig identities.

Sin²X + Cos²X = 1

tanX = sinX / cosX

For what range do solutions exist for sinx = k and cosx = k ?

-1 < k < 1

For what range do solutions exist for tanx = p?

All values of p

Describe how to solve equations in the form sin(nx) = k etc…

1. Change the interval so the centre is the same as the value given

2. Solve using the CAST diagram

3. Inverse the function to get the answer back in terms of x

How do you solve trigonometric equations in quadratic form?

Factorise and solve each bracket normally

Substitute the answers into the CAST diagram

Describe how to solve quadratic trig equations using the trig identity.

Replace the trig functions that are squared with the one that is not squared so that all the functions are the same

Then solve normally