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Angle function values, relationships

There are many relationships between the function values of the different angular functions, knowledge of which can be very advantageous for the investigation of theoretical relationships as well as for calculations - do my home work . This concerns both the function values of different angle functions for one and the same argument and the values of a certain angle function for different arguments.

There are many relationships between the function values of the different angular functions, the knowledge of which can be very advantageous for the investigation of theoretical relationships - https://domyhomework.club/algebra-homework/ - as well as for calculations. This concerns both the function values of different angular functions for one and the same argument as well as the values of a certain angular function for different arguments.

Correlation between the sine and cosine function values of the same angle

The figure in Figure 1 shows a quarter circle. The triangle OQP1 is right-angled and therefore follows:

sin^2 x + cos^2 x =1

This relation holds for all angles x (x≠k⋅π/2, k∈Z) and, because of 0^2+ 1^2=1^2+ 0^2=1, even applies to angles x=k⋅π/2, although then the above right triangle no longer exists.

Using the formula given as well as the relationship tan x=sin x/cos x, one can also calculate the values for the other two directly - pay someone to do math homework (i.e. without first determining the corresponding angle) from the function value of an argument for one of the three angle functions or set up corresponding formulae.

Example:

Given: sin x = 0.6

Wanted: cos x, tanx

cos^2 x =1-sin^2 x, thus cos x=√(1-0.6^2)=√0.64=0.8

tan x=0.6/0.8=0.75

This calculation refers to angles from the I. quadrant.

Without this restriction, cos x = -0.8 and thus additionally tan x = -0.75 would also have to be included.

In general, sin^2 x + cos^2 x =1 and tan x=sin x/cos x result in the following conversion formulae