** Answer: **

1. sinα = 12/13, tanα = 12/5, cosecα = 13/12

we will now solve question 2 together.

Solution to number 2

tan B = 2/3

tan^{2}B = 4/9

tan^{2}B + 1 = sec^{2}B

= sec^{2}B

= sec^{2}B

lcm is 9

root 9 is 3

but cosB = 1/secB

cosB =

since we already know tanB and cosB, we can easily get sinB using

tanB = sinB/cosB

3 cancel 3 at the denominator

divide both sides by

.

**EXAMPLE **

If cosA = 0.8, find the value of sinA and cotA.

__Solution__

Sin^{2}A + cos^{2}A = 1

Sin^{2}A + (0.8)^{2 }= 1

Sin^{2}A + 0.64 = 1 (collect like terms)

Sin^{2}A = 1 – 0.64

Sin^{2}A = 0.36 (take the square root of both sides)

**sinA = 0.6 **

cotA =

cot A =

cot A = 1.33

we can also get our cot a from

1 + cot^{2}A = cosec^{2}A

1 + cot^{2}A = (cosec^{2}A = )

1 + cot^{2}A = (Sin^{2}A = 0.36 before taking the roots of both sides from above)

1 + cot^{2}A = 2.7778

collect like terms

cot^{2}A = 2.7778 - 1

cot^{2}A = 1.7778

take the square root of both sides

cotA = 1.333 (same as our answer above)

** Exercise B**

Using trigonometric formulas only to solve these problems

1. If cos A = , find tan A and cosec^{2}A

2. Given that tan B = , find the value of cos B and cosec B

3. What is the value of tan C and cos C given that sin C =

4. Given that sec^{2}P = 1/9, find the value of cosP, sin P and cot^{2}P

5. If cot x = 3.7, evaluate sin x, cos x and sec x.

6. What is the value of tan^{2 }Y and sec Y when Sin Y = 2/5

7. If cot θ = 7, find the value of tan θ , sin θ and sec θ.

8. Find in terms of k sin θ and cos θ given that tan θ = k

9. If cosec α = find in terms of sec β and cot β.

10. if sec x = , what is the value of tan x and cosec x.

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