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ryanuser
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Why 1 divided by cos(pi/4)=cos(-pi/4)?
Is it wrong to say 1/cos(pi/4)=sec(pi/4)?
Thanks
Is it wrong to say 1/cos(pi/4)=sec(pi/4)?
Thanks
The thread title is now "Reciprocal of cos".Buzz Bloom said:BTW: The title of the thread does not match your question. The inverse of the cos is the arccos, which is not the same as the reciprocal, 1/cos.
The value of cos(-pi/4) is approximately 0.707, also known as the square root of 2 divided by 2. This value represents the cosine of the angle -pi/4, which is equivalent to a 45 degree angle in the fourth quadrant of a unit circle.
The value of sec(pi/4) is approximately 1.414, also known as the square root of 2. This value represents the secant of the angle pi/4, which is equivalent to a 45 degree angle in the first quadrant of a unit circle.
The main difference between cos(-pi/4) and sec(pi/4) is that they represent different trigonometric functions. Cosine is a ratio of the adjacent side to the hypotenuse in a right triangle, while secant is a ratio of the hypotenuse to the adjacent side. Additionally, cos(-pi/4) represents an angle in the fourth quadrant, while sec(pi/4) represents an angle in the first quadrant.
Yes, both values can be simplified to 1/√2. This simplification is possible because the cosine and secant of pi/4 are complementary trigonometric functions, meaning they have the same value when added to the other angle in a right triangle.
Cos(-pi/4) and sec(pi/4) are related by the reciprocal identity, which states that the cosine and secant of an angle are inverses of each other. In other words, cos(-pi/4)*sec(pi/4) = 1. This relationship can also be seen in the unit circle, where the x-coordinate (cosine) and the reciprocal of the y-coordinate (secant) are symmetrical about the line y=x.