Trig Ratios

Intro

In trigonometry, it is important to know the trig ratios to help solve certain problems dealing with the matters of angles, equations, degrees, unit circle, etc. There are six trig ratios.
Co-functions:
sin=opp/hyp csc=1/(opp/hyp)=hyp/opp
cos=adj/hyp sec=1/(adj/hyp)=hyp/adj
tan=opp/adj cot=1/(opp/adj)=adj/hyp

-Co-functions are trig ratios that are the inverses of SOH CAH TOA.
-sin=sine -csc=cosecant
-cos=cosine -sec=secant
-tan=tangent -cot=cotangent
-It is important to know the special triangle relationships with the degrees and the lengths to help us.
-It is better to draw these triangles, not just to memorize the degrees and lengths because memorization does not help in the long run.
-A 45-45-90 triangle has 1:1:√2 in terms of length.
-A 30-60-90 triangle has 1:√3:2 in terms of length.

Sample Problem

If f(x)=sin^2x+tan(x)-2, find the value of f(π/4).

Solution

1. Substitute x for π/4.
f(π/4)=sin^2(π/4)+tan(π/4)-2

2. Convert π/4 into degrees.
-Remember, in trig, π is 180 degrees.
f(45)=sin^2(45)+tan(45)-2

3. If we know that sin(45) is the square root of 2 over 2, then squaring it would be 1/2.
(√2 /2)^2= (√4 /4)= 2/4= 1/2
4. Since tan theta is opposite leg over adjacent leg, and this right triangle is a right isosceles triangle, then tan(45)= 1.

5. Plug in the answers for sin^2(45) and tan(45).
1/2 + 1 -2= 3/2-2= 3/2-4/2= -1/2



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