Find the exact value of the other five trigonometric functions.

Question

Given sin(a)=2/3 and cos(a)<0, find the exact value for the other 5 trig functions.

Answer 1

I'll help if you promise to draw a right triangle, deal?

Good.

Now that you've done that, place angle "A" in any corner that isn't a right angle. Remember the definition of SINE?

Sin Θ = opposite  / hypotenuse

That means the 2 is your opposite and the 3 is the hypotenuse. You'll need to use the Pythagorean Theorem to find the missing side (the adjacent):

A² + B² = C²

A² + 2² = 3²

A² + 4    = 9

     - 4       -4

A²           = 5

  A          = √5

There's the adjacent. All you have to do now is find the other five trig functions by creating fractions from the three sides. Oh -- one last detail, though: what sign does each have? Remember the rule: "A Smart Trig Class". In three quadrants, only two trig functions are positive: one of the original three as well as its reciprocal function, such as COS and SEC. In the first quadrant, all are positive.