trigonometry test STUDY STUDY STUDY STUDY

Question 1

What is the pythagorean theorem?

Answer 1

a2 + b2 = c2

Question 2

converse of the pythagorean theorem

Answer 2

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

Question 3

if a2 + b2 = c2

Answer 3

it is a right triangle

Question 4

if a2 + b2 > c2

Answer 4

it’s an acute triangle

Question 5

if a2 + b2 < c2

Answer 5

it is an obtuse triangle

Question 6

trig rules

Answer 6

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

Question 7

to find a missing side

Answer 7

use sin, cos, or tan

Question 8

to find a missing angle

Answer 8

use inverse sin, cos, or tan

Question 9

angle of elevation

Answer 9

angle at the bottom of the triangle

Question 10

angle of depression

Answer 10

angle at the top of the triangle

Question 11

right triangles in word problems (and in general)

Answer 11

height/altitude is perpendicular to the ground, and with kite questions, the string is straight

Question 12

the relationship between sine and cosine

Answer 12

sin (x) = cos (y) OR sin (x) = cos (90-x)

Question 13

what does it mean for the relationship of sine and cosine when 2 angles are complementary?

Answer 13

when 2 angles = 90, the sine of one angle is EQUAL to the cos of the other (they are simply the same)

Question 14

**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

Question 15

45-45-90 triangle theorem

Answer 15

both legs are congruent, the length of the hypotenuse is the square root of the leg

Question 16

30-60-90 triangle theorem

Answer 16

shorter leg- x
longer leg- cubic root of x
hypotenuse- 2x

Question 17

altitude proportions of a right triangle

Answer 17

seg 1/altitude = altitude/seg 2

Question 18

hypotenuse proportions

Answer 18

hypotenuse/leg = hypotenuse/leg projection

Question 19

law of sine for sides

Answer 19

a/sin A = b/sin B = sin/sin C

Question 20

law of cosine for sides

Answer 20

a2= b2 + c2 -2(b)(c)Cos(A)

Question 21

law of sine for angles

Answer 21

sinA/a = sinB/b = sinC/c

Question 22

law of cosine for angles

Answer 22

cos(A)= b2 + c2 - a2 /2bc

Question 23

When should law of sine be used

Answer 23

1) 2 angles and one side
2) 2 sides and a non included angle

Question 24

When should law of cosine be used

Answer 24

1) 3 sides
2) 2 sides and one angle- to find 3rd side