Radians/Degrees/Unit Circle Test

(reciprocal identities) sin0 =

1 / csc0 or y

(reciprocal identities) cos0 =

1 / sec0 or x

(reciprocal identities) tan0 =

1 / cot0 or y / x

(reciprocal identities) csc0 =

1 / sin0 or 1 / y

(reciprocal identities) sec0 =

1 / cos0 or 1 / x

(reciprocal identities) cot0 =

1 / tan0 or x / y

(quotient identities) tan0 =

sin0 / cos0

(quotient identities) cot0 =

cos0 / sin0

pythagorean identities formula

sin²0 + cos²0 = 1

label the formulas

x = x√3

y = x

z = 2x

label the formulas

x = x

y = x√3

z = 2x

label the formulas

x = x√2

y = x

z = x

label the exact answer (unit circle)

x = √3/2

y = ½

z = 1

label the exact answer (unit circle)

x = ½

y = √3/2

z = 1

label the exact answer (unit circle)

x = 1

y = √2/2

z = √2/2

π =

half circle (180°)

2π =

full circle (360°)

π/2 =

90° of the circle

3π/2 =

270° of the circle

π/3 =

60°

π/4 =

45°

π/6 =

30°

Acronym for sin, cos, and tan

SOH CAH TOA

How do you convert degrees into radians?

Multiply degree by π / 180

How do you convert radians into degrees?

Multiply radian by 180 / π

What’s the Pythagorean theorem?

a² + b² = c²

How would you solve a verify problem?

• Pick ONE side to start with (recommended most complicated side)

• Use the formulas you memorized and get that side to match the other

• Don’t try and solve the side all at once, start with one section at time, split the equation up if you have to.

When you are working on a word problem make make sure to…

• Check if the angle is elevation or depression

• The 2 angles that aren’t the 90 degree angle must add up 90 degrees

• Draw a picture

When doing a s = r * 0 problem make sure…

When you get the answer to r * 0 make sure to turn that answer into a radian using π / 180

What do you use when you have a word problem and you have both the adjacent and the opposite but you’re missing the theta (tan)?

Use the equation 0 = tan^-1(tan0)

(Note: you should be able to find tan0 because you have the adjacent and opposite)

What do you do when you have a word problem and you have the opposite and the theta (tan) but not the adjacent?

• Find the other angle across from the original theta. (They should add up to 90)

• Use the new theta and input that into the tan equation. tan(84) = o/a

• Multiply the bottom by both sides and you’ll get the answer

What do you do when you have a word problem and have the adjacent and the theta (tan) but the opposite is missing?

• Write out the tan equation. tan(55) = o/a

• You have adjacent so just multiply the adjacent by both sides

When you have a square root make sure to..

simplify it if it can be simplified

Don’t leave…

square roots at the bottom of the fraction, multiply it by itself.

When you have to solve for csc(90 - 0) = 3 what does that mean?

• You have a new theta, the one across from the original theta

• So for csc you’ll first find sin using the new theta and then sin will help you find csc

• Both theta’s have to add up to 90, so you should be able to find the new theta

You can simply fractions on your calculator using….

the math button

Quadrants are numbered using the ___ shape

C

When you have something like 6π/3 what can you do to find the quadrant and the shape?

You know just about how much space π/3 takes up so count 6 of those shapes around the unit circle and the general area should give you enough information to solve.

Practice counting π/3, π/4, and π/6

Make sure you know which is angle of elevation and which is angle of depression and how you can find the other angles using it.

30°, 45°, and 60° are separated by…

15 degrees, with this information you can find all the angles of the unit circle.