Vocab
Define complementary angles.
Two positive angles that add up to pi/2.
Convert pi/6 to degrees.
30
If opp. = 4 and adj. = 13 on a right triangle, find sin(theta).
sin(theta) = square root(185) or 13.60
What is THE most important trig identity we learned in this chapter?
sin2+cos2=1
How do you convert from radians to degrees?
Multiply by (180 deg. / pi)
Define supplementary angles.
Two positive angles that add up to pi.
Convert -pi/4 to degrees.
315 or -45
Write the side lengths (opp., adj., hyp.) of a 30-60-90 triangle.
opp = 1, hyp = 2, adj = square root(3)
What is secant?
1/cos or hyp./adj.
What is the reference angle for 5pi/6?
pi/6.
Two angles that have the same initial and terminal sides are called ______.
Coterminal
Convert 180 degrees to radians.
pi
What is special about a 45-45-90 triangle?
You can use either 45 angle to find the six trig functions.
What is the cosine value at 60 degrees?
1/2
Which quadrant does 5pi/6 lie in on the unit circle?
II
s=r(theta)
Convert 7pi/6 to degrees.
210
Construct a right triangle with a hypotenuse of 5 and adjacent of 3. Find the opposite side length.
4
What is the reference angle for theta = pi/2 degrees?
pi/2 since theta is in quadrant I.
Why would two triangles that look different have the same trig function values?
If they are similar triangles with corresponding sides.
Define standard position.
Initial side coincides with the positive x-axis.
What is the positive angle measure (in degrees) for -pi/6?
330
If theta is 37 degrees and the hypotenuse is 10.3, what is the opposite side length?
6.198
What is the reference angle for theta = 2.3?
pi - 2.3 = .8416 radians
How do we derive the trig identity 1 + cot2(theta) = csc2(theta)?
sin2+cos2=1 (divide by sin2)
1 +cot2=csc2