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

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Vocabulary Trigonometry Derived from Greek words meaning “triangle measurement”

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Triangle terminology

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Opposite side: the side opposite the angle angle opposite angle

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Adjacent side: the side beside the angle adjacent angle

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

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

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Definitio ns A B 90 o C a c b

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

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

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

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

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

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

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

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

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

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Find the value of x degrees using Trig. Note: When finding an angle measure use “inverse” Trig. or the 2nd button!! x 3 9 ____ x 16 ----- 20 x ____ 4 5 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 Since x is the angle, use the 2nd button! Type 2nd Tan, then 9/3 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 Sin, then 4/5 using the n/d button. 71.6 36.9 53.1

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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

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

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