8-4 Sine, Cosine, and Tangent Ratios

8-4Sine, Cosine, and Tangent Ratios Chapter 8 Section 4 Mrs. Brook 

Vocabulary • Derived from Greek words meaning “triangle measurement” • Trigonometry

Triangle terminology

Opposite side: the side opposite the angle angle opposite opposite opposite angle angle angle opposite

Adjacent side: the side beside the angle adjacent angle angle angle adjacent adjacent adjacent angle

Hypotenuse: the longest side and across from the right angle hypotenuse hypotenuse hypotenuse hypotenuse

SOH CAH TOA You need to memorize this!!! Use SOH CAH TOA to help you remember these ratios!!! • SOH • CAH • TOA

Definitions B c a A 90o C b

Sine of angle A opposite hypotenuse a c B sin(A) = = c a A 90o C b

Sine of angle B opposite hypotenuse b c B sin(B) = = c a A 90o C b

Cosine of angle A adjacent hypotenuse b c B cos(A) = = c a A 90o C b

Cosine of angle B adjacent hypotenuse a c B cos(B) = = c a A 90o C b

Tangent of angle A opposite adjacent a b B tan(A) = = c a A 90o C b

Tangent of angle B opposite adjacent b a B tan(B) = = c a A 90o C b

A 25 24 B C 7 Write the Sin, Cos, and Tan Ratios for angle A SOH CAH TOA Sin A = 7/25 Cos A = 24/25 Tan A = 7/24

Try this one  SOH CAH TOA Sin F Cos F Tan F 8/10 = 4/5 6/10 = 3/5 8/6 = 4/3 6/10 = 3/5 8/10 = 4/5 6/8 = 3/4 Sin E Cos E Tan E

Find the value of x using Trig. Note: If “x” is on top - multiply; If “x” is on bottom - divide!! Remember: SOH CAH TOA THIS IS JUST THE ANGLE!! Since we have an A & H we use Cos Cox 62 = 50/x Since we have an O & A we use Tan (no hypotenuse!) Tan 64 = x/7 Since we have an O & A we use Tan (no hypotenuse!) Tan 67 = 6/x Since we have an O & H we use Sin Sin 35 = x/20 62 50 ------ x 64 7 X ------ 67 x 6 ------ 35 ---- X 20 Since x is on bottom divide. Type 6 divided by tan 67 in calc Since x is on top, mult. Type 7 * tan 64 in calc. Since x is on top, mult. Type 20 * sin 35 in calc. Since x is on bottom divide Type 50 divided by cos 62 in calc.

Find the value of x degrees using Trig. Note: When finding an angle measure use “inverse” Trig. or the 2nd button!! Remember: SOH CAH TOA Since we have an O & A we use Tan (no hypotenuse!) Tan x = 9/3 Since we have an A & H we use Cos Cos x = 16/20 Since we have an O & H we use Sin Sin x = 4/5 x 3 9 ____ x 16 ----- 20 x ____ 4 5 71.6 36.9 53.1 Since x is the angle, use the 2nd button! Type 2nd Sin, then 4/5 using the n/d button. Since x is the angle, use the 2nd button! Type 2nd Cos, then 16/20 using the n/d button. Since x is the angle, use the 2nd button! Type 2nd Tan, then 9/3 using the n/d button.

What have I learned? SOH CAH TOA If “x” is on bottom “divide” If “x” is on top “multiply” If solving for a side use regular sin, cos, or tan If solving for an angle use inverse sin, cos, or tan

Here’s your daily joke  • Why didn’t sin and tan go to the party? Just cos Ha! Ha! 

8-4 Sine, Cosine, and Tangent Ratios