Download presentation

Presentation is loading. Please wait.

Published byQuinn Watson Modified over 3 years ago

1
**7-3 Sine and Cosine (and Tangent) Functions 7-4 Evaluating Sine and Cosine**

sin is an abbreviation for sine cos is an abbreviation for cosine tan is an abbreviation for tangent

2
**Which of the following represents r in the figure below**

Which of the following represents r in the figure below? (Click on the blue.) x P(x,y) r y Close. The Pythagorean Theorem would be a good beginning but you will still need to “get r alone.” You’re kidding right? (xy)/2 represents the area of the triangle! CORRECT!

3
**Which of the following represents sin in the figure below**

Which of the following represents sin in the figure below? (Click on the blue.) x P(x,y) r y Sorry. Does Some Old Hippy Caught Another Hippy Tripping on Acid sound familiar? y/x represents tan. Sorry. Does SohCahToa ring a bell? x/r represents cos. CORRECT! Well done.

4
**Which of the following represents cos in the figure below**

Which of the following represents cos in the figure below? (Click on the blue.) x P(x,y) r y CORRECT! Yeah! Oops! Try something else. Sorry. Wrong ratio.

5
**Which of the following represents tan in the figure below**

Which of the following represents tan in the figure below? (Click on the blue.) x P(x,y) r y CORRECT! Yeah! Try again. Try again.

6
**In your notes, please copy this figure and the following three ratios:**

x P(x,y) r y

7
**A few key points to write in your notebook: **

P(x,y) r x y A few key points to write in your notebook: P(x,y) can lie in any quadrant. Since the hypotenuse r, represents distance, the value of r is always positive. The equation x2 + y2 = r2 represents the equation of a circle with its center at the origin and a radius of length r. The trigonometric ratios still apply but you will need to pay attention to the +/– sign of each.

8
(–3,2) r –3 2 Example: If the terminal ray of an angle in standard position passes through (–3, 2), find sin and cos . You try this one in your notebook: If the terminal ray of an angle in standard position passes through (–3, –4), find sin and cos . Check Answer

9
**Example: If is a fourth-quadrant angle and sin = –5/13, find cos .**

Since is in quadrant IV, the coordinate signs will be (+x, –y), therefore x = +12.

10
**Example: If is a second quadrant angle and cos = –7/25, find sin .**

Check Answer

11
**Determine the signs of sin , cos , and tan according to quadrant**

Determine the signs of sin , cos , and tan according to quadrant. Quadrant II is completed for you. Repeat the process for quadrants I, III, and IV. Hint: r is always positive; look at the red P coordinate to determine the sign of x and y. P(–x,y) r y r x y P(x,y) x P(–x, –y) r x y P(x, –y) r x y

12
**Check your answers according to the chart below: **

All are positive in I. Only sine is positive in II. Only tangent is positive in III. Only cosine is positive in IV. y x All Sine Tangent Cosine

13
**A handy pneumonic to help you remember! Write it in your notes!**

Students All x Take Calculus

14
**Find the reference angle. Determine the sign by noting the quadrant.**

Let be an angle in standard position. The reference angle associated with is the acute angle formed by the terminal side of and the x-axis. y y P(–x,y) P(x,y) r r Find the reference angle. Determine the sign by noting the quadrant. Evaluate and apply the sign. x x y P(x, –y) r x y x r P(–x, –y)

15
**Example: Find the reference angle for = 135.**

Check Answer You try it: Find the reference angle for = 5/3. You try it: Find the reference angle for = 870. Check Answer

16
**Give each of the following in terms of the cosine of a reference angle:**

Example: cos 160 The angle =160 is in Quadrant II; cosine is negative in Quadrant II (refer back to All Students Take Calculus pneumonic). The reference angle in Quadrant II is as follows: =180 – or =180 – 160 = 20. Therefore: cos 160 = –cos 20 You try some: cos 182 cos (–100) cos 365 Check Answer Check Answer Check Answer

17
**Try some sine problems now: Give each of the following in terms of the sine of a reference angle:**

Check Answer Check Answer Check Answer Check Answer

18
**Can you complete this chart?**

60 30 45 60 30 45

19
**Check your work!!!!!! Write this table in your notes!**

20
**Give the exact value in simplest radical form.**

Example: sin 225 Determine the sign: This angle is in Quadrant III where sine is negative. Find the reference angle for an angle in Quadrant III: = – 180 or = 225 – 180 = 45. Therefore:

21
**You try some: Give the exact value in simplest radical form:**

sin 45 sin 135 sin 225 cos (–30) cos 330 sin 7/6 cos /4 Check Answer Check Answer Check Answer Check Answer Check Answer Check Answer Check Answer

22
Homework: Page , #1, 3, 11, 13, 15, 17

Similar presentations

OK

Then/Now You found values of trigonometric functions for acute angles using ratios in right triangles. (Lesson 4-1) Find values of trigonometric functions.

Then/Now You found values of trigonometric functions for acute angles using ratios in right triangles. (Lesson 4-1) Find values of trigonometric functions.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on changes around us for grade 6 Ppt on magnetic field lines class 10 Ppt on social contract theory of government Ppt on energy giving food for kids Ppt on energy crisis in india Ppt on steve jobs biography book Ppt on 2nd world war planes Ppt on cobb douglas production function Ppt on eisenmenger syndrome Ppt on multi sectoral approach on ncds