Day 6 – Six Trigonometric Functions 2

Objectives:At the end of the period, I should

be able to...• Find the six trigonometric

functions given the terminal side of angle in standard position passing through (x,y)

The six trigonometric functions are defined as follows:

Signs of Function Values

QIAll functions

positive

QIISine and cosecant positive

QIIITangent and cotangent positive

QIVCosine and

secant positive

Signs of Function Values

Example 1. Locate angle in the coordinate plane if is in standard position and the terminal side passes through point P (- 3, - 4).

x

y r

P(- 3, - 4)

●

Example 2. The terminal side of in standard position passes through (- 3, - 4). Find the values of the six trigonometric functions of .

x = - 3 ; y = - 4;

Group Activity

Three problems will be given, each group will answer the problem assigned to them• Groups 1, 2, 3: Answer Problem A • Groups 4, 5, 6: Answer Problem B • Groups 7, 8, 9, 10: Answer Problem C

Answers will be posted to padlet to the set they are tasked to answer

Problem A: http://padlet.com/jose_calamlam/pyfhgb0m336bProblem B: http://padlet.com/jose_calamlam/x7t9of6i9c2eProblem C: http://padlet.com/jose_calamlam/rejuyu7t7n9c

Group Activity

• Problem A: The terminal side of in standard position passes through (5,-12). Find the values of the six trigonometric functions of .

• Problem B: The terminal side of in standard position passes through (- 8, 6). Find the values of the six trigonometric functions of .

• Problem C: The terminal side of in standard position passes through (2, -5). Find the values of the six trigonometric functions of .

PROBLEM A: The terminal side of in standard position passes through (5,-12). Find the values of the six trigonometric functions of .

x = 5 ; y = - 12;

PROBLEM B: The terminal side of in standard position passes through (- 8, 6). Find the values of the six trigonometric functions of .

x = - 8 ; y = 6;

PROBLEM C: The terminal side of in standard position passes through (2, - 5). Find the values of the six trigonometric functions of .

x = 2 ; y = - 5;

Homework 3

Given the right triangle below, find the value of six trigonometric functions. Answer must be in simplified form

sin =

cos =

tan =

csc =

sec =

cot =

Homework

For you to answer the assignment you must watch the following videos (Khan Academy):

Using SOH-CAH-TOA: https://www.khanacademy.org/math/trigonometry/basic-trigonometry/basic_trig_ratios/v/example-using-soh-cah-toa

More examples: https://www.khanacademy.org/math/trigonometry/basic-trigonometry/basic_trig_ratios/v/basic-trigonometry-ii