Can someone please solve them,I just want to see examples,i will do the next 10 myself!!THX!

Question

1)given that tan θ = 2/3 and that θ is acute,find the exact value of:
a)sin θ
b)cos θ
c)sin^2 θ
2)given that sin given that tan θ = (√2)/5 and that θ is acute,find the exact value of:
d)sin θ + cos θ
e)(cos θ - tan θ) / (1 - cos^2 θ)

Answer 1

1)given that tan θ = 2/3 and that θ is acute,find the exact value of:
a)sin θ
b)cos θ
c)sin^2 θ
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Draw that right triangle
opposite = 2
adjacent = 3
so hypotenuse = sqrt(4+9) = sqrt 13
sin = opposite / hyp = 2/sqrt 13
cos = adjacent / hyp = 3/sqrt 13
sin^2 = 4/13

Answer 2

2)given that [ sin given that <---- huh ? ] tan θ = (√2)/5 and that θ is acute,find the exact value of:
d)sin θ + cos θ
e)(cos θ - tan θ) / (1 - cos^2 θ)
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opposite = sqrt 2
adjacent = 5
so hypotenuse = sqrt (27)
sin = sqrt(2/27)
cos = sqrt (25/27)
etc remember 1 - cos^2 = sin^2

Answer 3

Given: X = 3, Y = 2.
a. r^2 = x^2 + y^2 = 3^2 + 2^2 = 13
r = sqrt(13).
sin A = y/r = 2/sqrt(13).

b. Cos A = x/r = 3/sqrt(13).

c.

2. Given: X = 5, Y = sqrt(2).
r^2 = x^2 + y^2 = 5^2 + (sqrt(2))^2 = 27
r = 3sqrt(3).
d. sin A + cos A = sqrt(2)/3sqrt(3) + 5/3sqrt(3) = (sqrt(2)+5)/3sqrt(3).