if secΘ=4/3, and Θ is a first quadrant angle, find the value of sin Θ and tan Θ, I am really having a hard

Question

time understanding this and I am afraid I will not pass tomorrows final:( Please can someone explain in simple to understnd terms please

Answer 1

Hi,

sec Θ is the reciprocal of cos Θ.
csc Θ is the reciprocal of sin Θ.
cot Θ is the reciprocal of tan Θ.

If secΘ=4/3, then cos Θ= 3/4. Since cosine = adjacent over hypotenuse, the adjacent side is 3 and the hypotenuse is 4.
To find the opposite side, use the Pythagorean Theorem:
3² + b² = 4² becomes 9 + b² = 16. Solving b² = 7 and b = √7.
So the opposite side is √7.

Sin Θ = opposite/hypotenuse = √(7)/4
Cosine Θ = adjacent/ hypotenuse = 3/4
Tangent Θ = opposite/adjacent = √(7)/3
Cosecant Θ = hypotenuse/opposite = 4√(7)
Secant Θ = hypotenuse/adjacent = 4/3
Cotangent Θ = adjacent/opposite = 3/√(7)

I hope that helps you!!! :-)

Good luck tomorrow!!!

Answer 2

secΘ = 1/cos Θ
cos Θ =1/ secΘ
cos Θ = 1/(4/3)
cos Θ =3/4

draw triangle

hypotenuse =4
side = 3
opposite=?

let opposite be x

4^2 = 3^2 +x^2
x^2 = 4^2 - 3^2
x^2 = 16-9
x = sqrt 7

sin Θ = opposite /hypotenuse
sin Θ = sqrt 7 / 4#

tan Θ =opposite /side
tan Θ =sqrt 7 /3#

Answer 3

You just need to remember some trig identities:

sec = 1/cos, which also means cos = 1/sec
csc = 1/sin, which also means sin = 1/csc
cot = 1/tan, which also means tan = 1/cot

another good identity is:

tan = sin/cos

still another is

sin^2 + cos^2 = 1
tan^2 + 1 = scs^2
1 + cot^2 = csc^2

Now to solve your problem: find sin
sec = 4/3
by identity cos = 1/sec = 1/(4/3) = 3/4
use sin^2 + cos^2 = 1
sin^2 + (3/4)^2 = 1
sin^2 + 9/16 = 1
sin^2 = 1 - 9/16 = 7/16
sin = sqrt(7/16) = sqrt(7)/4=.6614
now find tan:
tan = sin/cos = sqrt(7)/4 divided by 3/4

tan = sqrt(7)/ 3 = .8819

Answer 4

1/cos Ó¨ = 4/3
cos Ó¨ = 3/4
Vertical side = √(4²-3²) = √7
sin Ө = √7/4
tan Ө = √7/3