Question
Solve the equation $tan~x+ \sqrt 3= 0$ for $0^{\circ}\leq x\leq360^{\circ}.$
▶️Answer/Explanation
$120, \, 300
$
$
\tan x + \sqrt{3} = 0
$
$
\tan x = -\sqrt{3}
$
$
\tan x = \pm \sqrt{3} \implies \text{Reference angle} = 60^\circ
$
Since the value is negative, the solutions will be in Quadrants II and IV .
In Quadrant II:
$
x = 180^\circ – 60^\circ = 120^\circ
$
In Quadrant IV:
$
x = 360^\circ – 60^\circ = 300^\circ
$
Question
Solve the equation $8\sin x+ 6= 1$ for $0^{\circ}\leqslant x\leqslant360^{\circ}.$
▶️Answer/Explanation
$218.7,321.3$
$
8 \sin x + 6 = 1
$
$
8 \sin x = 1 – 6
$
$
8 \sin x = -5
$
$
\sin x = -\frac{5}{8}
$
$
\theta = \sin^{-1}\left(\frac{5}{8}\right)
$
$
\theta \approx 38.68^\circ
$
Since the sine value is negative, the solutions are in the third and fourth quadrants
Third quadrant
$
x = 180^\circ + 38.68^\circ = 218.68^\circ
$
Fourth quadrant
$
x = 360^\circ – 38.68^\circ = 321.32^\circ
$
Question
(a)Calculate the area of triangle ABC.
……………………………….\(cm^{2}\)
(b)Calculate the length of AC.
AC=………………………cm
Answer/Explanation
(a)20.1 or 20.07 to 20.08
(b)5.86 or 5.858
Question
(a) Calculate the area of triangle PQR.
…………………………………….\(cm^2\)
(b) Triangle PQR is enlarged by scale factor 4.5 .
Calculate the area of the enlarged triangle……………………………………..\(cm^2\)
Answer/Explanation
Ans:
(a) 11.4 or 11.40 to 11.41
(b) 231 or 230.8 to 231.1
Question
Use the sine rule to find angle ABC.
Angle ABC = ……………………………………….
Answer/Explanation
19.3 or 19.26 to 19.27
Question
Calculate the area of the triangle.
cm2 [2]
Answer/Explanation
Ans:
13 45[.0] or 44.99 to 45.00
Question
(a) Find the area of triangle ABC.
……………………………………… \(m^{2}\)
(b) Calculate AC
Answer/Explanation
(a)2.24
(b) 3.22 or 3.224 to 3.225