Trigonometry SOHCAHTOA

Triangle Facts Write down everything you know about triangles. Include any vocabulary related to triangles that you may have learned. Include Diagrams. Be Creative….

Triangle Facts Write down everything you know about triangles. +three sides, three angles, three corners(vertex or vertices), not a good wheel, strongest shape, sum of all angles is 180 degrees, isoceles, scalene, equilateral, right angle, obtuse, acute, pythagoras theorem (a squared + b squared= c squared), only works on Right angled triangles, pie or cheese, pizza, toblerone, legend of zelda triforce, hypoteneuse, legs

Can you think of a Nick Name for Right Angled Triangles? I like the Nick Name RATS!

Three Sided Baseball Diamond Imagine the pitcher stands at the pitcher’s mound at one of the acute angles. S/he throws the ball to the side which is opposite to him/her. opposite Pitcher’s Mound

Three Sided Baseball Diamond From the opposite side, the player throws the ball to the player at the hypotenuse. hypoteneuse 3 opposite 2 Pitcher’s Mound 1

Three Sided Baseball Diamond The player at the hypotenuse throws the ball to the last side of the triangle which is the adjacent. Hypoteneuse 3 Opposite 2 Pitcher’s Mound 1 4 Adjacent

The Three Sides of a Triangle Every right angled triangle has three sides labelled from a reference angle. Hypoteneuse Opposite Reference Angle Adjacent

The Three Sides of a Triangle What happens if we move the reference angle? Discuss this with a partner? How does this change the labels on the sides? Reference Angle

The Three Sides of a Triangle The adjacent and the opposite are switched! The Hypotenuse stays the same! Reference Angle Hypotenuse—doesn’t change! Adjacent Opposite

Label the sides of the RATS: Label all the three sides from the reference angle. A H O H O A

What is the side called? A A

The Three Trig Ratios

Understanding the Notation

TRIGONOMETRY Mnemonic Here is a quick way to remember the sides that correspond to each ratio. S O H C A H T O A

What are these buttons for? Have you noticed three buttons on your calculator? Sin Cos Tan These buttons relate to the three trig ratios we have shown from the RATS.

What are these buttons for? Sin Cos Tan The calculator can calculate the ratio for any given angle instantly. Find the sin 98 °. You may need to determine if you press the sin button or enter 98 first. Try this on your calculator: Answer is: 0.990268068

Did you get the wrong answer? Check to see if your calculator is in the wrong mode. ✔ Right Mode: Degree, D, Deg ✗ Wrong Modes: Grad, Rad Find your Mode Button to change it to Degrees and try the question again. Mode

What are these buttons for? Sin Cos Tan Find the following ratios using your calculator to 4 decimals: sin 45°= cos 60°= tan 57°= 0.7071 0.5 1.5398

What are these buttons for? Sin-1 Cos-1 Tan-1 These buttons help you find the angle if you are given the trig ratio. I call this ‘going backwards’. Find the above buttons on your calculator. They may be above your sin/cos/tan keys. You may need to use a Second Function Key or another key to access these additional functions on your calculator.

What are these buttons for? Sin-1 Cos-1 Tan-1 Let’s try the following example. Find the angle if: Method 1: Enter 4 ⁄ 5 on your calculator and enter second function sin Method 2: Enter second function sin ( 4 ⁄ 5) on your calculator ANSWER: 53.13 degrees

Let’s do a question! What are the three trig ratios from the reference angle. 5 3 4

Trigonometry Ratios

Try this question! Find the three ratios from the following triangle. ✔ 14 12 8

Answers

Which Ratio Do You Use? S O H C A H T O A √ Starting at the reference angle decide which two sides you have. Pick the trig ratio that uses those two sides.  7 15 H O ✔A

Which Ratio Do You Use? Ask yourself: What sides do I have? Which Trig Ratio uses those two sides!  6 ✔B 25

Which Ratio Do You Use?  Ask yourself: What sides do I have? Which Trig Ratio uses those to sides!  36 ✔C 25

Case 1: What if you are given one angle and one side and need to find the missing side? Find the missing side x. 56° 20 X

Case 1: What is the side you have and what is the side you need? Have: Hypoteneuse Need: Adjacent Use the Cosine Ratio 56° 20 X

Case 1: Fill in the Cosine Ratio with the given side and the angle. 56° 20 X

Case 1: Solve for the value of x. 56° 20 X

Case 2: What if you are given one angle and one side and need to find the missing side? Find the missing side x. 35° x 12

Solution: What is the side you have and what is the side you need? Have: Opposite Need: Hypotenuse Use the Sine Ratio 35° x 12

Solution: The ratio that uses both the O and the H is the sin ratio. 12 is the opposite side X is the hypotenuse 35°

Solution: Now we can fill in the ratio: 35° X 12

Solution: Now we can fill in the ratio: Solve for x in the above equation by using the ‘Switcheroo’

Summarizing Case 1 and Case 2 If the side you are missing is in the NUMERATOR such as: Then multiply the two values together x=sin 43 x 12

Summarizing Case 1 and Case 2 If the side you are missing is in the DENOMINATOR such as: Then use the ‘switcheroo’ to switch the cos 43 and the x Answer would be 7÷(cos 43)

Summarizing Case 1 and Case 2 Case 1: Multiply × Case 2: Switcheroo ÷

THE END I hope this was everything you needed to know about trigonometry!