HardMathematicsHigh School (11–12)Trigonometry › Trigonometric Functions and Graphs Trigonometry › Trigonometric IdentitiesNumericalConceptualBoard Exam AP A-Level IB

For which values of x with 0 ≤ x < 2π is sin x = cos x?

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

For which values of $x$ with $0 \le x < 2\pi$ is $\sin x = \cos x$ ? How many such values are there, and what is the smaller one, to 3 decimal places?

Need a reminder? The key ideaShow

On the unit circle, the point reached by turning through $x$ from $A(1, 0)$ is $P = (\cos x, \sin x)$ . So $\sin^2 x + \cos^2 x = 1$ , and $1 + \tan^2 x = \sec^2 x$ . The sign of $\cos x$ is the sign of the x-coordinate of $P$ , and the sign of $\sin x$ is the sign of its y-coordinate.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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