Equation sin θ = cos θ Solution
We need to find the value of the angle $\theta$ in degrees, given the trigonometric equation $\sin \theta = \cos \theta$.
Steps to Solve sin θ = cos θ
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Start with the given equation:
$ \sin \theta = \cos \theta $
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Divide both sides by $\cos \theta$. This is valid as long as $\cos \theta \neq 0$.
$ \frac{\sin \theta}{\cos \theta} = \frac{\cos \theta}{\cos \theta} $
$ \frac{\sin \theta}{\cos \theta} = 1 $
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Apply the tangent trigonometric identity, which states that $\tan \theta = \frac{\sin \theta}{\cos \theta}$. The equation simplifies to:
$ \tan \theta = 1 $
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Identify the angle $\theta$ in degrees for which the tangent value is 1. This angle is:
$ \theta = 45^{\circ} $
We confirm our assumption: $\cos(45^{\circ}) = \frac{\sqrt{2}}{2}$, which is not zero, validating the division step.
Final Answer Value
The value of $\theta$ that satisfies $\sin \theta = \cos \theta$ is $45^{\circ}$.
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If cosec θ = 13/12, then sin θ + cos θ - tan θ is equal to:
What is the value of \(\frac{3 \sin 58^{\circ}}{\cos 32^{\circ}}+\frac{3 \sin 42^{\circ}}{\cos 48^{\circ}}\) ?
If \(\frac{{\tan \theta + \sin \theta }}{{\tan \theta - \sin \theta }} = \frac{{k + 1}}{{k - 1}},\) then k = ?
If α + β = 90° and α = 2β, then the value of 3 cos 2 α - 2 sin 2 β is equal to:
If \(\sqrt{3}\) tan θ = 3 sin θ, then what is the value of sin 2θ − cos 2θ ?
