using csc = 3.75, solve for sides:
a= 3
b= ?
c= ?
and the remaining five trigonometric functions:
sin= (1/3.75)
cos= ?
tan= ?
sec= ?
cot= ?
*b is not 1; and c is not 3.75
You need an "argument" after csc and sin
e.g. csc Ø = 3.75 = 375/100 = 15/4
then sin Ø = 4/15
so that particular triangle has sides
4 , √209 , and hypotenuse 15
since I cannot tell which sides you labeled a , b, and c
other than the hypotenue is usually labeled c
I will take a stab that the side of a=3 matches the 4 of my triangle
so
3 : b : c = 4 : √209 : 15
3/4 = c/15
c = 45/4
and
b/√209 = 3/4
b = 3√209/4
(for the second part , again sin = (1/3.75) is just that, a mathematical sin)
from above
sin Ø = 4/15
cos Ø = √209/15
tan Ø = 4/√209
sec Ø = 15/√209
cot Ø = √209/4
csc Ø = 15/4 or 3.75
To solve for sides a, b, and c using the given values csc = 3.75 and a = 3, we can start by finding the values of sin, cos, and tan.
1. Given csc = 3.75, we know that cscθ = 1/sinθ. Plugging in the value, we get:
1/sinθ = 3.75
To find sinθ, we take the reciprocal of csc:
sinθ = 1/3.75
2. To find cosθ, we can use the Pythagorean identity:
sin²θ + cos²θ = 1
Since we have sinθ as 1/3.75, we can solve for cosθ:
(1/3.75)² + cos²θ = 1
cos²θ = 1 - (1/3.75)²
cosθ = sqrt(1 - (1/3.75)²)
3. Finally, to find tanθ, we can use the relationship between sinθ and cosθ:
tanθ = sinθ / cosθ
tanθ = (1/3.75) / cosθ
Now, let's solve for b and c:
Given that a = 3:
a = b
3 = b
b = 3
Since c is not equal to 3.75, we cannot determine its value with the given information.
Now, let's find the remaining five trigonometric functions:
1. secθ = 1/cosθ (Reciprocal of cosθ)
2. cotθ = 1/tanθ (Reciprocal of tanθ)
By substituting the values we obtained for sinθ and cosθ, we can calculate secθ and cotθ accordingly.
Please note that finding the exact value of cosθ, secθ, and cotθ would require a calculator to compute the square root and division accurately.