The angles \(A\) and \(B\) are complementary angles to each other if \(A + B = 90^{\circ}\). Hence,
Given that \(\text{sin } 77^{\circ} = 0.9744\) and \(\text{cos } 77^{\circ} = 0.225\).
Find the value of \(\text{cos }13^{\circ}\).
Given \(\text{cos }63^{\circ} = k\), where \(k \text{ > }0\).
Find the value of \(\text{cosec }27^{\circ}\) in terms of \(k\).
Method 1: Use a calculator
The values of sine, cosine and tangent can be determined by using a calculator
The values for cosecant, secant and cotangent can be calculated by inversing the values of the trigonometric ratios of sine, cosine and tangent
Method 2: Use a unit circle
Use the unit circle above and state the value of \(\text{cos }135^{\circ}\).
The coordinates that correspond to \(135^{\circ}\) are
\(\begin{pmatrix} -\dfrac{1}{\sqrt2}, \ \dfrac{1}{\sqrt2} \end{pmatrix}\) and \(\text{cos }135^{\circ} = x\text{-coordinate}\).
Hence, \(\text{cos }135^{\circ} = -\dfrac{1}{\sqrt2}\).
Method 3: Use the corresponding trigonometric ratio of the reference angle
Method 4: Use a right-angled triangle
The trigonometric ratios of special angles \(30^{\circ}, 45^{\circ} \text{ and }60^{\circ}\) can be determined by using right-angled triangles
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