Trigonometric functions HELP PLEASE?

Well, let's draw a graph.

|

|......☻

|....../ |

|..c/...| 4

|../.....|

|/.Θ__|_____

...2

So, we have a right triangle. The first thing we'll do is find the hypotenuse, using the Pythagorean theorem.

c^2 = 4^2 + 2^2

c^2 = 16 + 4

c^2 = 20

c = √20

c = 2√5

So, the sine of angle Θ is equal to the opposite side length divided by the hypotenuse. The cosine is equal to the adjacent side divided by the hypotenuse. The tangent is equal to the opposite side over the adjacent side.

sin Θ = 4 / (2√5) = 2√5 / 5

cos Θ = 2 / (2√5) = √5 / 5

tan Θ = 4 / 2 = 2

Now, the cosecant is equal to 1 over the sine. The secant is 1 over the cosine, and the cotangent is 1 over the tangent.

csc Θ = 1 / sin Θ = 2√5 / 4 = √5 / 2

sec Θ = 1 / cos Θ = 2√5 / 2 = √5

cot Θ = 1 / tan Θ = 2 / 4 = 1/2

I hope that helps!

the three undemanding trig purposes are sin, cos, and tan. imagine about a excellent triangle, with angles A, B = ninety ranges, and C. opposite those angles are the perimeters a, b, and c. Then sin(A) = a / b And cos(A) = c / b And tan(A) = a / c The "area" of a function is the numbers that you'll positioned into the function. For sin, cos, and tan, you are able to put in any form (any attitude). The area is -infinity to + infinity. The "decision" is the numbers that you get out of the function. sin(...) is continually contained in the decision -a million to +a million. cos(...) is continually contained in the decision -a million to +a million. tan(...) is continually contained in the decision -infinity to +infinity.

x = 2

y = 4

r = √(x^2 + y^2) = √(4 + 16) = √20 = 2√5

sin θ = y/r = 2/√5

csc θ = r/y = √5/2

cos θ = x/r = 1/√5

sec θ = r/x = √5

tan θ = y/x = 2

cot θ = x/y = 1/2

(2,4) means x=2, y=4 and so hyp=√(2^2 +4^2) =2√5

Remember also that:

sinθ=y/hyp =4/2√5=2/√5

cosθ=x/hyp=2/2√5 =1/√5

tanθ=y/x =4/2 =2