Trigonometry Chapters

Theorem

The opposite sides of a triangle are the same length Using the Pythagorean theorem we find the hypotenuse is always n times the square root of 2

Theorem What is the length of the hypotenuse

Theorem What is the length of the hypotenuse

Theorem What is the length of the sides?

Theorem What is the length of the sides? Remember, the hypotenuse is  2 times a side

Divide by  2 Rationalize the Denominator

Theorem

The opposite of the 30 0 angle is n

Theorem The opposite of the 60 0 angle is n  3

Theorem The opposite of the right angle is 2n

Theorem Find the lengths of the other two sides

Theorem Find the lengths of the other two sides

Theorem Find the lengths of the other two sides

Theorem Find the lengths of the other two sides

Theorem Find the lengths of the other two sides First find the length of side opposite the 30

Theorem Call the side x x times  3 = 8

Theorem Hypotenuse is 2 times the side opposite the 30 0 angle

Trigonometry Trigonometric Ratios- – Similar right triangles have equivalent ratios for its corresponding sides

Sine Sine of óB =

Sine Sine of óB =

Sine Sin B =

Cosine Cosine of óB =

Cosine Cosine of óB =

Cosine Cos B =

Tangent Tangent of óB =

Tangent Tangent of óB =

Tangent Tan B =

Trigonometry How to remember the order: Sin x = Cos x = Tan x =

Trigonometry Find the sine, cosine, and tangent ratios of ó B

Sin B = Cos B = Tan B =

Trigonometry What is the sin of ó B? Type it into a calculator: sin (40) Sin (40) =.64

How can we use this? Find the length of the hypotenuse. We’re given angle B and the opposite side

We know: We can plug in what we know: Find the length of the hypotenuse. Sin B = Sin 40 =

Solve: Sin 40 = Sin 40 =

Plug it into your calculator to find x Sin 40 = =

Find the length of the adjacent side. Cos B = Cos 40 =

Solve for x Cos 40 = Type into calculator 9.19 =

Find the length of the adjacent side =

Inverse Trig Functions Each trig function has an inverse that works like dividing. The inverse of sin is sin -1

Inverse Trig Functions

Find angle x Label the triangle

We have the opposite and hypotenuse Which one uses those two sides? Sin x = Cos x = Tan B =

Plug in the opposite and hypotenuse Sin x = Notice the x is in front of the sine, so we can’t just divide! Multiply by the inverse of sine

This cancels out the sine on the left Sin -1 (Sin x) = Sin -1