Question
If $\tan\theta=\frac{24}{7},$ find that $\sin\theta+\cos\theta.$
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Answer
$\tan\theta=\frac{24}{7}$ find $\sin\theta+\cos\theta$
Let x - 1 be the hypotenuse By applying Pythagoras theorem we get
$\text{AC}^2=\text{AB}^2+\text{BC}^2$ $\text{x}^2=(24)^2+(7)^2$ $\text{x}^2=576+49=62.5$ $\text{x}=25$ $\sin\theta=\frac{\text{AB}}{\text{AC}}=\frac{24}{25}$ $\cos\theta=\frac{\text{BC}}{\text{AC}}=\frac{7}{25}$ $\sin\theta+\cos\theta=\frac{24}{25}+\frac{7}{25}$ $=\frac{31}{25}$
Let x - 1 be the hypotenuse By applying Pythagoras theorem we get
$\text{AC}^2=\text{AB}^2+\text{BC}^2$ $\text{x}^2=(24)^2+(7)^2$ $\text{x}^2=576+49=62.5$ $\text{x}=25$ $\sin\theta=\frac{\text{AB}}{\text{AC}}=\frac{24}{25}$ $\cos\theta=\frac{\text{BC}}{\text{AC}}=\frac{7}{25}$ $\sin\theta+\cos\theta=\frac{24}{25}+\frac{7}{25}$ $=\frac{31}{25}$
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