Trig Functions

Trig Geometry

Dr. Tom Giles

Draw

The side across from the RIGHT ANGLE is called the HYPOTENUSE.

Draw

The side that connects the RIGHT ANGLE to your reference angle (THETA) is the side ADACENT.

Draw

The side across from THETA is the side OPPOSITE.

Draw

Label each side with H, A and O

Trigonometry is just a

RATIO of 2 sides of a right triangle. So we can set it up as

TRIG(angle) = fraction​

Remember your SOH-CAH-TOA??

S O/H C A/H T O/A

SINE COSINE TANGENT

SINE = OPPOSITE/HYPOTENUESE

​

COSINE = ADJACENT/HYPOTENUESE

​

TANGENT = OPPOSITE/ADJACENT​

Multiple Choice

Which ratio represent $$\sin\left(\theta\right)$$ ?

sine = opp/hyp

• 8/10

• 6/10

• 8/6

• 6/8

Multiple Choice

Which ratio represents $$\cos\left(\theta\right)$$ ?

cos = adj/hyp

• 8/10

• 6/10

• 8/6

• 6/8

Multiple Choice

Which ratio represents $$\tan\left(\theta\right)$$  ?

tan = opp/adj

• 8/10

• 6/10

• 8/6

• 6/8

Multiple Choice

Which ratio represents $$\tan\left(\theta\right)$$  ?

• 8/17

• 8/15

• 15/17

• 15/8

Multiple Choice

Which ratio represents $$\cos\left(\theta\right)$$  ?

• 15/8

• 15/17

• 8/15

• 8/17

Multiple Choice

Which ratio represents $$\sin\left(\theta\right)$$  ?

• 8/17

• 15/17

• 8/15

• 15/8

​Evaluate Sin/Cos/Tan

Be sure your calculator is in the correct MODE. For all of the Trigonometry applications we will use, make sure you are in DEGREE mode.

Calculator -- hit MODE scroll down and select DEGREE.

Desmos -- click on the WRENCH top right corner and select DEGREE.

**Default mode for calculators is RADIAN mode, so make sure your calculator is in DEGREE mode.

Subject | Subject

Fill in the Blanks

What is $\sin\left(42^0\right)$   rounded to 3 decimal places?

Fill in the Blanks

What is $\tan\left(220^0\right)$   rounded to 3 decimal places

Ready to solve for a missing side?​

Start by labeling your sides OPP, ADJ & HYP according to the reference angle (usually labeled or has a measure). Which side has a measure​? Which side are you solving? This will let you know if you are using SIN, COS, or TAN.

TRIG (angle) = side / side Fill in what you know and solve!​

Subject | Subject

Multiple Choice

Solve for side b

• 3.73 m

• 7.25 m

• 3.38 m

• 0.06 m

Fill in the Blanks

Solve for x rounding to the nearest tenth (1 decimal place)

​Ready to solve for a missing angle?

Like before, label all your sides according to your reference angle (the one you are solving for). Determine if you will use SIN, COS, or TAN. This time you are using an inverse function (the angle and the ratio trade places).

If using a calculator, 2nd SIN/COS/TAN. If using Desmos, click on FUNCTIONS​, Inverse Trig​.

TRIG^-1 (SIDE/SIDE) = missing angle​

Subject | Subject

You got this!!

Multiple Choice

Solve for x:

x = ____⁰

• 51

• 39

• 54

• 36

Fill in the Blanks

Solve for angle A, rounding to the nearest whole number. Angle A =

⁰

Poll

How would you describe your understanding of Trig Geometry?

• I am completely lost

• I think I got some of it but need help

• I think I got it and am going to practice some more

• I got it and I can help others