Tan37.5
The angles 37, 52, and 90 correspond to a 3,4,5 sided right angled triangle.
Using that information, you can take tan37.5 = 3/4
Use a calculator for a more accurate value.
this is probably a question asking for EXACT values
37.5 = 1/2 of 75
and 75 = 30+45
so find tan75 = tan(30+45)
= (tan30 + tan45)/( 1 - tan30*tan45)
= (1/√3 + )/(1 - 1/√3)
= (1+√3)(√3 - 1)
recall tan 2A = 2tan A/(1 - tan^2 A)
tan 75 = 2tan37.5/(1-tan^2 37.5)
let tan37.5 = x
(1+√3)(√3 - 1) = 2x/(1-x^2)
(1+√3)(1-x^2) = 2x(√3 - 1)
expand, collect like terms and you will have a quadratic.
Use the quadratic formula to find the exact value.
I know it looks messy but stick to it
use the addition formula as above to find
sin(75) = sin45*cos30+cos45*sin30 = (√3-1)/√8
cos(45) = cos45*cos30-sin45*sin30 = (√3-1)/√8
Now using the half-angle formula,
tan(37.5) = (1-cos75)/sin75 = sin75/(1+cos75)
No quadratics to solve, but you still have messy algebra.
To find the value of tangent (tan) of 37.5 degrees, you can follow these steps:
1. Convert 37.5 degrees to radians:
To convert degrees to radians, you need to multiply the degree measure by π/180.
In this case, 37.5 * (π/180) = 0.654498469 radians.
2. Use a scientific calculator or a trigonometric table:
Most calculators have trigonometric functions built-in. If you have a scientific calculator, simply enter 37.5 and press the "tan" button. It should give you the result directly.
Alternatively, you can use trigonometric tables specifically designed for angles. These tables provide the values of trigonometric functions for different angles, including tangent. To use the table, locate the row corresponding to 37.5 degrees and look for the value in the column for tangent.
3. Using a calculator, without built-in tangent function:
If you don't have a calculator with a tangent function or a trigonometric table, you can use the tangent identity:
tan(x) = sin(x) / cos(x)
For this specific case:
We know that sin(37.5 degrees) = 0.601815023 and cos(37.5 degrees) = 0.79863551.
So, tan(37.5 degrees) = sin(37.5 degrees) / cos(37.5 degrees) = 0.601815023 / 0.79863551 = 0.75355405
Therefore, the value of tangent (tan) 37.5 degrees is approximately 0.75355405.