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**8-4 Sine, Cosine, and Tangent Ratios**

Chapter 8 Section 4 Mrs. Brook

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**Vocabulary Derived from Greek words meaning “triangle measurement”**

Trigonometry

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Triangle terminology

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

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**Adjacent side: the side beside the angle**

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

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

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Definitions B c a A 90o C b

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

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

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

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

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

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

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**Write the Sin, Cos, and Tan Ratios for angle 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 F Sin E Cos F Cos E Tan F Tan E SOH CAH TOA**

6/10 = 3/5 8/10 = 4/5 6/8 = 3/4 Sin F Cos F Tan F 8/10 = 4/5 6/10 = 3/5 8/6 = 4/3 Sin E Cos E Tan E

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**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 64 7 X ------ 67 x 6 ------ 35 ---- X 20 62 50 ------ x Since x is on top, mult. Type 7 * tan 64 in calc. 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!! 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 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.

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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 cos Ha! Ha!

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The study of triangles Relationship between sides and angles of a right triangle › What is a right triangle? A triangle with a 90 ⁰ angle 90°

The study of triangles Relationship between sides and angles of a right triangle › What is a right triangle? A triangle with a 90 ⁰ angle 90°

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