Worksheet Week 2.1 & 2 - SSSS PDF

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MATH 112-SP20 Worksheet - Week 6 Section 2.1 & 2.2

Part 1 (Fill in the blanks):

a) Simplifying the expression tan(−𝜃) tan 𝜃 + 𝑠𝑒𝑐 2 𝜃, we get ________________. b) An ___________ is an equation that is true for all values of the variable for which the expressions in the equation are defined. c) A ______________ equation is an equation that is true for only some values of the variable. d) A contradiction is an equation that is ____________ for any value of the variable.

Part 2 (MCQ): Choose the correct answer for the following questions: 2

1. Find the value of sin(𝑥), given that cot 𝑥 = 3 and 𝑥 is an angle in quadrant III. 4

(b) −

(a) 13

4

(c) −

13

5 2. If cos 𝑥 = − 13. Find the value of 1 + tan2 𝑥.

(a)

25

169

(b)

169

2 √13

5

(c) 17

25

(d) −

13

(d)

17 5

3. If tan 𝑥 = 2 , and 𝑥 in quadrant I. Find the values of cos2 𝑥 − cos 𝑥 sin 𝑥. 1

(a) − 5

(b)

4. If sec 𝑥 = 3 find the values of 2

2 2

tan2 𝑥∙cos 𝑥 , sin3 𝑥 3

(b) −

(a) 3

(c)

5

2√2

Verify the given identities:

a) 𝑐𝑜𝑠2 𝑥 + 𝑡𝑎𝑛2 𝑥 + 𝑠𝑖𝑛2 𝑥 − 𝑠𝑒𝑐 2 𝑥 = 0

c)

tan 𝑥+cot 𝑥 sec 𝑥+csc 𝑥 1+sin 𝑥 1+csc 𝑥

Science Track

=

1 sin 𝑥+cos 𝑥

= sin 𝑥

(d)

2 √5

𝑥 in quadrant IV.

Part 2: (Essay Question)

b)

1 5

(c)

1 3

(d)

2 √2

3√13 13...