For the equation $$\(3 \tan ^{2} x-5 \tan x+k=0\)$$, state the value of $$\(k\)$$ for which there are three solutions in the interval $$\(0^{\circ} \leqslant x \leqslant 180^{\circ}\)$$, and find these solutions. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m20_qp_12 Year：2020 Question No：11(c)
Answer:
\[
\begin{array}{l}
k=0\\
\tan x=0 \text { or } \frac{5}{3}
\end{array}
\]
\(x=0^{\circ}\) or \(180^{\circ}\) or \(59.0^{\circ}\)
\begin{array}{l}
k=0\\
\tan x=0 \text { or } \frac{5}{3}
\end{array}
\]
\(x=0^{\circ}\) or \(180^{\circ}\) or \(59.0^{\circ}\)
Knowledge points:
1.5.1 sketch and use graphs of the sine, cosine and tangent functions (for angles of any size, and using either degrees or radians)
1.5.5 find all the solutions of simple trigonometrical equations lying in a specified interval (general forms of solution are not included).
Solution:
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