Funatic Maths

Written on
- Paper 2

Question 5

5.15.1 Simplify the following expression to ONE trigonometric term:
sin⁡xcos⁡x.tan⁡x+sin⁡(180∘+x)cos⁡(90∘−x)\frac{\displaystyle\sin{x}}{\displaystyle\cos{x}.\tan{x}}+\sin(180^{\circ}+x)\cos(90^{\circ}-x)		 (5)(5)
5.25.2 Without using a calculator\textbf{Without using a calculator}, determine the value of:
sin⁡235∘−cos⁡235∘4sin⁡10∘cos⁡10∘\frac{\displaystyle \sin^2 35^{\circ}-\cos^2 35^{\circ}}{\displaystyle 4\sin 10^{\circ}\cos 10^{\circ}}		 (4)(4)
5.35.3 Given: cos⁡26∘=m\cos 26^{\circ}=m
Without using a calculator\textbf{Without using a calculator}, determine 2sin⁡277∘2\sin^2 77^{\circ} in terms of mm.		 (4)(4)
5.45.4 Consider: f(x)=sin⁡(x+25∘)cos⁡15∘−cos⁡(x+25∘)sin⁡15∘f(x)=\sin(x+25^{\circ})\cos 15^{\circ}-\cos(x+25^{\circ})\sin 15^{\circ}
5.4.1\quad 5.4.1 Determine the general solution of f(x)=tan⁡165∘f(x)=\tan 165^{\circ} (6)(6)
5.4.2\quad 5.4.2 Determine the value(s) of xx in the interval x∈[0∘ ; 360∘]x\in[0^{\circ}\,;\,360^{\circ}] for which f(x)f(x) will have a minimum value. (3)(3)
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