Show:
Coterminal Angles and Quadrants
Trig Ratios and the Pythagorean Theorem
Converting Between Radians and Degrees
Unit Circle Trig Ratios
Definitions
100
Give a positive coterminal angle for 10˚
370˚, 730˚, ...
100
Find the cosine of ø in the triangle on the board
Based on board
100
What is π/3 in degrees?
60˚
100
Evaluate sin( π/4 )
sqrt(2)/2
200
Find a positive coterminal angle for -5825˚
295˚, 655˚, ...
200

What is the length of the legs of an isosceles right triangle with a hypotenuse of 2?

sqrt(2)

200
What is 5π/4 in degrees?
225˚
200
Evaluate cos (11π/6)
sqrt(3)/2
200
What is the sine of an angle?
-A ratio in a right triangle equivalent to the opposite side over the hypotenuse. -In a unit circle, it is the y-coordinate for any given point on the circle
300
Find a negative coterminal angle for 89π/17
-13π/17 , -47π/17, ...
300
The one leg of a triangle is 6 inches and the hypotenuse is 8 inches. Find the length of the other leg.
sqrt(28) or 2sqrt(7)
300
What is 57π/60 in degrees?
171˚
300
Evaluate tan (3π / 4)
-1
300

What is the tangent of an angle?

-A ratio in a right triangle equivalent to the opposite side over the adjacent side. -In the unit circle, it is the y-coordinate divided by the x-coordinate for any given point on the circle

400
In what quadrant is the angle 103π/15 located?
QII (coterminal to 13π/15)
400
The length of one side of a triangle is 2a and the length of the other side is 2a. Find the length of the hypotenuse
2a*sqrt(2) or sqrt(8a^2)
400
What is 390˚ in radians (as a fraction in simplest form)?
13π/6
400

Evaluate cos (-4π/3)

-1/2

400
What is a coterminal angle?
An angle that looks identical to another angle in standard position but whose terminal side has been rotated by a multiple of 360˚ or 2pi
500
In what quadrant is the angle 7 located?
Q I (There are ~6.28 radians in a complete circle, so 7 radians is QI)
500
The lengths of the legs of a triangle are 24, 26, and 10. Is this a right triangle?
Yes-- 24^2 + 10^2 = 26^2
500
What is 204˚ in radians (as a fraction in simplest form)?
17π/15
500

Evaluate tan (π/2)

undefined

500

What is the Unit Circle?

-A circle drawn on a coordinate plane centered at the origin with a radius of 1.