Fouss math class wiki

Section 3 - Right Triangle Trig

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4.3 Right Triangle Trigonometry

TRIG RATIOS

SOHCAHTOA

(sine-opp./hyp.;cosine-adj./hyp.;tangent-opp./adj.)

The sides of a right triangle (the hypotenuse, the opposite side, and the adjacent side) are all relative to the angle (theta) , as represented by the six trig ratios.

Six Trig Ratios:

* Cosecant is the reciprocal of Sine; where Sine=opposite over hypotenuse, Cosecant=hypotenuse over opposite.

* Secant is the reciprocal of Cosine; where Cosine=adjacent over hypotenuse, Secant=hypotenuse over adjacent.

* Cotangent is the reciprocal of Tangent; where Tangent=opposite over adjacent, Cotangent=adjacent over opposite.

When given the angle and length of one side, you can find the missing sides and angle, using the trig ratios and the Pythagorean Therom.

ex. find the values of a, b, and c from the values above.

Using the answers to the sides from the triangle above, list the six trig ratios according to the 53.13 degree angle.

Given the length of the sides of a right triangle, you can find the measure of an angle using inverse functions.

SPECIAL RIGHT TRIANGLES

45,45,90

***[warning: if you use the radian instead of the degree when typing into your calculator do NOT forget to use the radian mode (on calc. hit mode then switch to radians 3 rows down)]

The ratio of the sides of a 45, 45, 90 triangle is (leg, leg, hypotenuse)

30,60,90

The ratio of the sides of a 30, 60, 90 triangle is:

(leg opposite 30, leg opposite 60, hypotenuse)

TRIG IDENTITIES

The trig identities are used to find sine, cosine, tangent, cosecant, secant, and cotangent when given the value of one or more trig ratios and even information to know which quadrant the angle is in. When given the value(s) of a trig ratio, insert to one of the following equations and solve for the other 5 ratios algebraically.

IDENTITIES: