trigonometry test STUDY STUDY STUDY STUDY
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What is the pythagorean theorem?
a2 + b2 = c2
converse of the pythagorean theorem
if the square of the length of one side of a triangle equals the sum of the squares of the lengths of the other two sides, the triangle is a right triangle
if a2 + b2 = c2
it is a right triangle
if a2 + b2 > c2
it’s an acute triangle
if a2 + b2 < c2
it is an obtuse triangle
trig rules
soh cah toa only works for right triangles, and the hypotenuse is always across from the right angle **be sure to have calc in degree mode
to find a missing side
use sin, cos, or tan
to find a missing angle
use inverse sin, cos, or tan
angle of elevation
angle at the bottom of the triangle
angle of depression
angle at the top of the triangle
right triangles in word problems (and in general)
height/altitude is perpendicular to the ground, and with kite questions, the string is straight
the relationship between sine and cosine
sin (x) = cos (y) OR sin (x) = cos (90-x)
what does it mean for the relationship of sine and cosine when 2 angles are complementary?
when 2 angles = 90, the sine of one angle is EQUAL to the cos of the other (they are simply the same)
**reminder when doing word problems when someone/an object is 1.5 feet above the water/ground you need to either add or subtract accordingly
45-45-90 triangle theorem
both legs are congruent, the length of the hypotenuse is the square root of the leg
30-60-90 triangle theorem
shorter leg- x longer leg- cubic root of x hypotenuse- 2x
altitude proportions of a right triangle
seg 1/altitude = altitude/seg 2
hypotenuse proportions
hypotenuse/leg = hypotenuse/leg projection
law of sine for sides
a/sin A = b/sin B = sin/sin C
law of cosine for sides
a2= b2 + c2 -2(b)(c)Cos(A)
law of sine for angles
sinA/a = sinB/b = sinC/c
law of cosine for angles
cos(A)= b2 + c2 - a2 /2bc
When should law of sine be used
1) 2 angles and one side 2) 2 sides and a non included angle
When should law of cosine be used
1) 3 sides 2) 2 sides and one angle- to find 3rd side